International Journal of Engineering Technologies (IJET) Volume: 2 No: 3 Printed ISSN: 2149-0104 September 2016 e-ISSN: 2149-5262 © Istanbul Gelisim University Press, 2016 Certificate Number: 23696 All rights reserved. International Journal of Engineering Technologies is an international peer–reviewed journal and published quarterly. The opinions, thoughts, postulations or proposals within the articles are but reflections of the authors and do not, in any way, represent those of the Istanbul Gelisim University. CORRESPONDENCE and COMMUNICATION: Istanbul Gelisim University Faculty of Engineering and Architecture Cihangir Mah. Şehit P. Onb. Murat Şengöz Sk. No: 8 34315 Avcilar / Istanbul / TURKEY Phone: +90 212 4227020 Ext. 221 Fax: +90 212 4227401 e-Mail: ijet@gelisim.edu.tr Web site: http://ijet.gelisim.edu.tr http://dergipark.ulakbim.gov.tr/ijet Twitter: @IJETJOURNAL Printing and binding: Anka Matbaa Sertifika No: 12328 Tel: +90 212 5659033 - 4800571 e-Posta: ankamatbaa@gmail.com ii International Journal of Engineering Technologies (IJET) is included in: International Journal of Engineering Technologies (IJET) is harvested by the following service: Organization URL Starting Feature Date https://www.openaire.eu/ 2015 Open Access The OpenAIRE2020 Project iii INTERNATIONAL JOURNAL OF ENGINEERING TECHNOLOGIES (IJET) International Peer–Reviewed Journal Volume 2, No 3, September 2016, Printed ISSN: 2149-0104, e-ISSN: 2149-5262 Owner on Behalf of Istanbul Gelisim University Rector Prof. Dr. Burhan AYKAÇ Editor-in-Chief Prof. Dr. İlhami ÇOLAK Associate Editors Dr. Selin ÖZÇIRA Dr. Mehmet YEŞİLBUDAK Layout Editor Seda ERBAYRAK Proofreader Özlemnur ATAOL Copyeditor Mehmet Ali BARIŞKAN Contributor Ahmet Şenol ARMAĞAN Cover Design Tarık Kaan YAĞAN iv Editorial Board Professor Ilhami COLAK, Istanbul Gelisim University, Turkey Professor Dan IONEL, Regal Beloit Corp. and University of Wisconsin Milwaukee, United States Professor Fujio KUROKAWA, Nagasaki University, Japan Professor Marija MIROSEVIC, University of Dubrovnik, Croatia Prof. Dr. Şeref SAĞIROĞLU, Gazi University, Graduate School of Natural and Applied Sciences, Turkey Professor Adel NASIRI, University of Wisconsin-Milwaukee, United States Professor Mamadou Lamina DOUMBIA, University of Québec at Trois-Rivières, Canada Professor João MARTINS, University/Institution: FCT/UNL, Portugal Professor Yoshito TANAKA, Nagasaki Institute of Applied Science, Japan Dr. Youcef SOUFI, University of Tébessa, Algeria Prof.Dr. Ramazan BAYINDIR, Gazi Üniversitesi, Turkey Professor Goce ARSOV, SS Cyril and Methodius University, Macedonia Professor Tamara NESTOROVIĆ, Ruhr-Universität Bochum, Germany Professor Ahmed MASMOUDI, University of Sfax, Tunisia Professor Tsuyoshi HIGUCHI, Nagasaki University, Japan Professor Abdelghani AISSAOUI, University of Bechar, Algeria Professor Miguel A. SANZ-BOBI, Comillas Pontifical University /Engineering School, Spain Professor Mato MISKOVIC, HEP Group, Croatia Professor Nilesh PATEL, Oakland University, United States Assoc. Professor Juan Ignacio ARRIBAS, Universidad Valladolid, Spain Professor Vladimir KATIC, University of Novi Sad, Serbia Professor Takaharu TAKESHITA, Nagoya Institute of Technology, Japan Professor Filote CONSTANTIN, Stefan cel Mare University, Romania Assistant Professor Hulya OBDAN, Istanbul Yildiz Technical University, Turkey Professor Luis M. San JOSE-REVUELTA, Universidad de Valladolid, Spain Professor Tadashi SUETSUGU, Fukuoka University, Japan Associate Professor Zehra YUMURTACI, Istanbul Yildiz Technical University, Turkey v Dr. Rafael CASTELLANOS-BUSTAMANTE, Instituto de Investigaciones Eléctricas, Mexico Assoc. Prof. Dr. K. Nur BEKIROGLU, Yildiz Technical University, Turkey Professor Gheorghe-Daniel ANDREESCU, Politehnica University of Timisoara, Romania Dr. Jorge Guillermo CALDERÓN-GUIZAR, Instituto de Investigaciones Eléctricas, Mexico Professor VICTOR FERNÃO PIRES, ESTSetúbal/Polytechnic Institute of Setúbal, Portugal Dr. Hiroyuki OSUGA, Mitsubishi Electric Corporation, Japan Professor Serkan TAPKIN, Istanbul Arel University, Turkey Professor Luis COELHO, ESTSetúbal/Polytechnic Institute of Setúbal, Portugal Professor Furkan DINCER, Mustafa Kemal University, Turkey Professor Maria CARMEZIM, ESTSetúbal/Polytechnic Institute of Setúbal, Portugal Associate Professor Lale T. ERGENE, Istanbul Technical University, Turkey Dr. Hector ZELAYA, ABB Corporate Research, Sweden Professor Isamu MORIGUCHI, Nagasaki University, Japan Associate Professor Kiruba SIVASUBRAMANIAM HARAN, University of Illinois, United States Associate Professor Leila PARSA, Rensselaer Polytechnic Institute, United States Professor Salman KURTULAN, Istanbul Technical University, Turkey Professor Dragan ŠEŠLIJA, University of Novi Sad, Serbia Professor Birsen YAZICI, Rensselaer Polytechnic Institute, United States Assistant Professor Hidenori MARUTA, Nagasaki University, Japan Associate Professor Yilmaz SOZER, University of Akron, United States Associate Professor Yuichiro SHIBATA, Nagasaki University, Japan Professor Stanimir VALTCHEV, Universidade NOVA de Lisboa, (Portugal) + Burgas Free University, (Bulgaria) Professor Branko SKORIC, University of Novi Sad, Serbia Dr. Cristea MIRON, Politehnica University in Bucharest, Romania Dr. Nobumasa MATSUI, Faculty of Engineering, Nagasaki Institute of Applied Science, Nagasaki, Japan Professor Mohammad ZAMI, King Fahd University of Petroleum and Minerals, Saudi Arabia Associate Professor Mohammad TAHA, Rafik Hariri University (RHU), Lebanon Assistant Professor Kyungnam KO, Jeju National University, Republic of Korea Dr. Guray GUVEN, Conductive Technologies Inc., United States Dr. Tuncay KAMAŞ, Eskişehir Osmangazi University, Turkey vi From the Editor Dear Colleagues, On behalf of the editorial board of International Journal of Engineering Technologies (IJET), I would like to share our happiness to publish the seventh issue of IJET. My special thanks are for members of editorial board, editorial team, referees, authors and other technical staff. Please find the seventh issue of International Journal of Engineering Technologies at http://dergipark.ulakbim.gov.tr/ijet. We invite you to review the Table of Contents by visiting our web site and review articles and items of interest. IJET will continue to publish high level scientific research papers in the field of Engineering Technologies as an international peer- reviewed scientific and academic journal of Istanbul Gelisim University. Thanks for your continuing interest in our work, Professor ILHAMI COLAK Istanbul Gelisim University icolak@gelisim.edu.tr -------------------------------------------- http://dergipark.ulakbim.gov.tr/ijet Printed ISSN: 2149-0104 e-ISSN: 2149-5262 vii viii Table of Contents Page From the Editor vii Table of Contents ix Elastostatic Deformation Analysis of Thick Isotropic Beams by Using Different Beam Theories and a Meshless Method Armagan Karamanli 83-93 Development of a Lidar System Based on an Infrared RangeFinder Sensor and SlipRing Mechanism Gokhan Bayar, Alparslan Uludag 94-99 Calculation and Optimizing of Brake Thermal Efficiency of Diesel Engines Based on Theoretical Diesel Cycle Parameters Safak Yildizhan, Vedat Karaman, Mustafa Ozcanli, Hasan Serin 100-104 Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics Armagan Karamanli 105-117 Fluorescent Lamp Modelling and Electronic Ballast Design by the Support of Root Placement Ibrahim Aliskan, Ridvan Keskin 118-123 Dynamic Spectrum Access: A New Paradigm of Converting Radio Spectrum Wastage to Wealth Jide J. Popoola, Oluwaseun A. Ogunlana, Ferdinad O. Ajie, Olaleye Olakunle, Olufemi A. Akiogbe, Saint M. Ani-Initi, Sunday K. 124-131 Omotola ix International Journal of Engineering Technologies, IJET e-Mail: ijet@gelisim.edu.tr Web site: http://ijet.gelisim.edu.tr http://dergipark.ulakbim.gov.tr/ijet Twitter: @IJETJOURNAL x INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 Elastostatic Deformation Analysis of Thick Isotropic Beams by Using Different Beam Theories and a Meshless Method Armagan Karamanli*‡ *Department of Mechatronics Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, 34215 Istanbul, Turkey. (afkaramanli@gelisim.edu.tr) ‡ Corresponding Author; Armagan Karamanli, Department of Mechatronics Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, 34215 Istanbul, Turkey, Tel: +90 2124227020, armagan_k@yahoo.com Received: 17.05.2016 Accepted: 27.07.2016 Abstract-The elastostatic deformations of thick isotropic beams subjected to various sets of boundary conditions are presented by using different beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The analysis is based on the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories. The performance of the SSPH method is investigated for the comparison of the different beam theories for the first time. For the numerical results, various numbers of nodes are used in the problem domain. Regarding to the computed results for RBT, various number of terms in the Taylor Series Expansions (TSEs) is employed. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections are carried out with the analytical solutions. It is found that the SSPH method has provided satisfactory convergence rate and smaller L2 error. Keywords Meshless Method, Element-Free, Beam, Euler-Bernoulli, Timoshenko, Reddy-Bickford. 1. Introduction thickness. The SCF depends on the geometric and material parameters of the beam but the loading and boundary The kinematics of deformation of a beam can be conditions are also important to determine the SCF [1-2]. In represented by using various beam theories. Among them, the third order shear deformation theory which is named as the Euler Bernoulli Beam Theory (EBT), the Timoshenko the RBT, the transverse shear strain is quadratic trough the Beam Theory (TBT) and the Reddy-Bickford Beam Theory thickness of the beam [3]. (RBT) are commonly used. The effect of the transverse shear The need for the further extension of the EBT is raised deformation neglected in the EBT is allowed in the latter two for the engineering applications of the beam problems often beam theories. characterized by high ratios, up to 40 for the composite Euler Bernoulli Beam Theory is the simplest beam structures, between the Young modulus and the shear theory and assumes that the cross sections which are normal modulus [4]. Various higher order beam theories are to the mid-plane before deformation remain plane/straight introduced in which the straightness assumption is removed and normal to the mid-plane after deformation. Both and the vanishing of shear stress at the upper and lower transverse shear and transverse normal strains are neglected surfaces are accommodated. For this purpose, higher order by using these assumptions. In the TBT, the normality polynomials incorporating either one, or more, extra terms assumption of the EBT is relaxed and the cross sections do [5-11] or trigonometric functions [12-13] or exponential not need to normal to the mid-plane but still remain plane. functions [14] are included in the expansion of the The TBT requires the shear correction factor (SCF) to longitudinal point-wise displacement component through the compensate the error due to the assumption of the constant thickness of the beam. The higher order theories introduce transverse shear strain and shear stress through the beam additional unknowns that make the governing equations 83 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 more complicated and provide the solutions much costly in In view of the above, the objectives of this paper mainly terms of CPU time. The theories which are higher than the are to present the SSPH method formulation for the isotropic third order shear deformation beam theory are seldom used thick beams subjected to different boundary conditions because the accuracy gained by these theories which require within the framework of EBT, TBT and RBT, to perform much effort to solve the governing equations is so little [4]. numerical calculations to obtain the transverse deflections of the studied beam problems and finally to compare the results The beam theories are still the reference technique in obtained by using the SSPH method with analytical many engineering applications. They continue to be solutions. It is believed that researchers will probably find advantageous in the analysis of slender bodies such as the SSPH method helpful to solve their engineering airplane wings, helicopter blades, bridges and frames where problems. the cumbersome two-dimensional 2D (plate and shell theories) and three-dimensional 3D analysis require higher In section 2, the formulation of the EBT, TBT and RBT cost and computational effort because of their complexity. is. In section 3, the formulation of the SSPH method is given for 1D problem. In Section 4, numerical results are given Meshless methods are widely used in static and dynamic based on the two types of engineering beam problem which analyses of the engineering beam problems [15-20]. To are a simply supported beam under uniformly distributed obtain the approximate solution of the problem by a meshless load and a cantilever beam under the uniformly distributed method, the selection of the basis functions is almost the load. The performance of the SSPH method is compared most important issue. The accuracy of the computed solution with the analytical solutions. can be increased by employing different number of terms in TSE or increasing number of nodes in the problem domain or 2. Formulation of Beam Theories by increasing the degree of complete polynomials. Many meshless methods have been proposed by researchers to To describe the EBT, TBT and RBT, the following obtain the approximate solution of the problem. The coordinate system is introduced. The x-coordinate is taken Smoothed Particle Hydrodynamics (SPH) method is along the axis of the beam and the z-coordinate is taken proposed by Lucy [21] to the testing of the fission through the height (thickness) of the beam. In the general hypothesis. However, this method has two important beam theory, all the loads and the displacements (u,w) along shortcomings, lack of accuracy on the boundaries and the the coordinates (x,z) are only the functions of the x and z tensile instability. To remove these shortcomings, many coordinates. [4] The formulation of the EBT, TBT and RBT meshless methods have been proposed such as the Corrected are given below. Smoothed Particle Method [22,23], Reproducing Kernel Particle Method [24-26], Modified Smoothed Particle 2.1. Euler Bernoulli Beam Theory Hydrodynamics (MSPH) method [27-30], the Symmetric Smoothed Particle Hydrodynamics method [31-36] and the Strong Form Meshless Implementation of Taylor Series The following displacement field is given for the EBT, Method [37-38], Moving Kringing Interpolation Method [39- 𝑑𝑤 40], the meshless Shepard and Least Squares (MSLS) 𝑢(𝑥, 𝑧) = −𝑧 𝑑𝑥 Method [42], Spectral Meshless Radial Point Interpolation (SMRPI) Method [42]. 𝑤(𝑥, 𝑧) = 𝑤0(𝑥) (1) It is seen form the above literature survey regarding to where w0 is the transverse deflection of the point (x,0) which the SSPH method, there is no reported work on the is on the mid-plane (z=0) of the beam. By using the elastostatic deformations of the thick isotropic beams assumption of the smallness of strains and rotations, the only subjected to the different boundary conditions by employing the axial strain which is nonzero is given by, the TBT and RBT. 𝑑𝑢 𝑑2𝑤 𝜀 = = −𝑧 0𝑥𝑥 2 (2) 𝑑𝑥 𝑑𝑥 Linear elastic problems including quasi-static crack propagation [31-33], crack propagation in an adhesively The virtual strain energy of the beam in terms of the bonded joint [34], 2D Heat Transfer problems [35] and 1D axial stress and the axial strain can be expressed by 4th order nonhomogeneous variable coefficient boundary 𝐿 value problems [36] have been successfully solved by 𝛿𝑈 = ∫ ∫ 𝜎𝑥𝑥𝛿𝜀𝑥𝑥𝑑𝐴𝑑𝑥 (3) 0 𝐴 employing the SSPH method. where δ is the variational operator, A is the cross sectional The SSPH method has an advantage over the MLS, area, L is the length of the beam, 𝜎𝑥𝑥 is the axial stress. The RKPM, MSPH and the SMITSM methods because basis bending moment of the EBT is given by, functions used to approximate the function and its derivatives are derived simultaneously and even a constant 𝑀𝑥𝑥 = ∫ 𝑧𝜎 𝑑𝐴 (4) 𝐴 𝑥𝑥 weight function can be employed to obtain the approximate By using equation (2) and equation (4), equation (3) can solution [31-36]. The matrix to be inverted for finding kernel be rewritten as, estimates of the trial solution and its derivatives is 2 asymmetric in the MSPH. In SSPH method which made the 𝐿 𝑑 𝛿𝑤𝛿𝑈 = − ∫ 𝑀𝑥𝑥𝑧 0 2 (5) matrix to be inverted symmetric, reduced the storage 0 𝑑𝑥 requirement and the CPU time. 84 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 The virtual potential energy of the load q(x) which acts By using equation (14) and equation (16), one can at the central axis of the beam is given by rewrite equation (15) as, 𝐿 𝐿 𝑑𝛿𝜙 𝑑𝛿𝑤 𝛿𝑉 = − ∫ 𝑞(𝑥)𝛿𝑤0𝑑𝑥 (6) 𝛿𝑈 = ∫ [ 𝑀𝑥𝑥 + 𝑄 (𝛿𝜙 + 0 𝑥 )] 𝑑𝑥 (17) 0 0 𝑑𝑥 𝑑𝑥 If a body is in equilibrium, δW=δU+δV, the total virtual The virtual potential energy of the load q(x) which acts work (δW) done equals zero. Then one can obtain, at the central axis of the Timoshenko beam is given by 𝐿 𝑑2𝛿𝑤 𝐿 𝛿𝑊 = − ∫ ( 𝑀 0𝑥𝑥𝑧 2 + 𝑞(𝑥)𝛿𝑤0) 𝑑𝑥 = 0 (7) 𝛿𝑉 = − ∫ 𝑞(𝑥)𝛿𝑤0𝑑𝑥 (18) 0 𝑑𝑥 0 After performing integration for the first term in Since the total virtual work done equals zero and the equation (7) twice and since 𝛿𝑤0 is arbitrary in (0 < x < L), coefficients of 𝛿𝜙 and 𝛿𝑤0 in 0 6 𝑑𝑥 𝑥𝑥 𝑑𝑥 𝑠 𝑥𝑧 𝑑𝑥 𝑑 𝑑𝑤 𝑑 = |𝑥 − 𝜉|/ℎ (50) − [𝜅 0𝑠𝐴𝑥𝑧 (𝜙 + )] = 𝑞0 (45) 𝑑𝑥 𝑑𝑥 where 𝑑 is the radius of the CSD, ℎ is the smoothing length. where 𝐷𝑥𝑥 = 𝐸𝐼𝑦 is the flexural rigidity of the beam, G and 𝜆 are the parameters which are eliminated by the 𝐼 = 𝑏ℎ3𝑦 /12 is the second moment of area about the y- formulation of the SSPH method. axis, 𝐴𝑥𝑧 = 𝐺𝐴 = 𝐺𝑏ℎ is the shear rigidity and the SCF is The numerical solutions are performed according to the assumed to be constant 𝜅𝑠 = 5/6 for the rectangular cross following meshless parameters; the radius of the support section. 87 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 domain (d) is chosen as 6 and the smoothing length (h) in Table 2 that the SSPH method almost gives the exact equals to 1.1∆ where ∆ is the minimum distance between two solution of the problem. The SSPH method gives accurate adjacent nodes. The meshless parameters, d and h, are values of the displacement even for 21 nodes in the problem selected to obtain the lowest error. domain. It is observed in Fig. 4 that the SSPH method agrees very well with the analytical solution. For the numerical solutions based on the formulation of the RBT, it is also investigated the effect of the different Table 2. L2 error norm for different number of nodes based numbers of terms employed in the TSE when the number of on TBT nodes in the problem domain increases. Computed results Meshless Number of Nodes obtained by using the SSPH method are compared with the Method 21 Nodes 41 Nodes 161 Nodes analytical solutions, and their accuracy and convergence -10 -9 -9 properties are investigated by employing the global L SSPH 4.3044x10 3.7090x10 3.5981x10 2 error norm which is given in equation (51). 1/2 2 [∑𝑚 𝑗 𝑗 𝑗=1(𝑣 2 ‖ ‖ 𝑛𝑢𝑚 −𝑣𝑒𝑥𝑎𝑐𝑡) ] 𝐸𝑟𝑟𝑜𝑟 2 = 1/2 (51) 𝑗 0 [∑𝑚 2𝑗=1(𝑣𝑒𝑥𝑎𝑐𝑡) ] SSPH - 5 term - 21 Node - TBT -2 SSPH - 5 term - 41 Node - TBT The L2 error norms of the numerical solutions based on SSPH - 5 term - 161 Node - TBT the EBT are given in Table 1. For the numerical analysis -4 Analytical Solution - TBT different numbers of nodes are considered in the problem domain with 5 terms in TSEs expansion. It is observed in -6 Table 1 that the accuracy of the SSPH method is not -8 improved by increasing of the number of nodes in the problem domain. At least for the problem studied here, it is -10 impossible to evaluate the convergence rate of the SSPH method because of the level of the numerical errors which -12 0 0.5 1 1.5 2 are too small obtained for different number of nodes in the Length Along Beam (m) problem domain. Fig. 4. Deflections of the beam computed based on the TBT It is observed in Fig. 3 that the SSPH method agrees very and the analytical solution well with the analytical solution. The transverse deflection of The global L2 error norms of the solutions based on the the beam computed by the SSPH method is virtually RBT are given in Table 3 where different numbers of nodes indistinguishable from that for the analytical solution. are considered with varying number of terms in TSEs Table 1. L error norm for different number of nodes based expansion. The results in Table 3 are obtained for the 2 on EBT meshless parameters d and h which gives the best accuracy for each method. Different numbers of terms in TSEs, 5 to 7, Meshless Number of Nodes are employed to evaluate the performance of the SSPH Method 21 Nodes 41 Nodes 161 Nodes method. It is found that the convergence rate of the computed -9 -8 -7 SSPH 3.8563x10 9.0440x10 3.6898x10 solution increases by increasing the degree of complete polynomials. The rate of convergence for the SSPH method increases by increasing the number of nodes in the problem domain. It is clear that numerical solutions obtained by the SSPH method agree very well with the analytical solution given in Fig. 5 to Fig. 7. Table 3. L2 error norm for different number of nodes with varying number of terms in the TSEs Terms in the TSEs Nodes 5 Term 6 Term 7 Term 21 2.0631 2.0475 2.0014 41 2.0631 2.0317 1.6977 161 2.0631 1.9371 0.5556 Fig. 3. Deflections of the beam computed based on the EBT Comparison of the analytical solutions in terms of and the analytical solution transverse deflections obtained by the EBT, TBT and RBT are given in Fig. 8. It is observed that the analytical solution The global L2 error norms of the solutions based on the obtained by the EBT is similar to the analytical solution TBT are given in Table 2 where different numbers of nodes obtained by the RBT than the TBT. It is clear that the RBT is are considered with 5 terms in TSEs expansion. The results a higher order shear deformation theory that yields more in Table 2 are obtained for the meshless parameters d and h accurate results than the other theories which are studied in which give the best accuracy for each method. It is observed this paper. 88 Deflection (mm) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 -2 -10 0 SSPH - 5 term - 21 Node - RBT -2 -1 SSPH - 5 term - 41 Node - RBT -10 SSPH - 5 term - 161 Node - RBT -4 Analytical Solution - RBT 0 -6 -10 EBT Analytical Solution -8 TBT Analytical Solution 1 -10 RBT Analytical Solution -10 2 -12 -10 0 0.5 1 1.5 2 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Length Along Beam (m) h/L Ratio (m) Fig. 5. Deflections of the beam computed based on the RBT Fig. 9. Comparison of the analytical solutions in terms of and the analytical solution – 5 term maximum deflections obtained with varying h/L ratio For the future studies, the effect of the h/L ratio can be 0 investigated to evaluate the accuracy of the TBT in terms of -2 SSPH - 6 term - 21 Node - RBT transverse deflection. In Fig. 8, the h/L ratio is 0.1. It is SSPH - 6 term - 41 Node - RBT observed in Fig. 9 that when the h/L ratio increases the -4 SSPH - 6 term - 161 Node - RBT Analytical Solution - RBT accuracy of the TBT decreases in terms of transverse deflection. -6 -8 4.2. Cantilever Beam -10 For a cantilever beam the static transverse deflections -12 under uniformly distributed load of intensity 𝑞0 as shown in 0 0.5 1 1.5 2 Length Along Beam (m) Figure 10 is studied. Fig. 6. Deflections of the beam computed based on the RBT z and the analytical solution – 6 term q 0 0 b -2 SSPH - 7 term - 21 Node - RBT x h SSPH - 7 term - 41 Node - RBT -4 SSPH - 7 term - 161 Node - RBT Analytical Solution - RBT -6 L -8 Fig. 10. Simply supported beam with uniformly distributed -10 load -12 0 0.5 1 1.5 2 The physical parameters are given as L=2m, h=0.2m, Length Along Beam (m) b=0.02m. Modulus of elasticity E is 210 GPa, shear modulus Fig. 7. Deflections of the beam computed based on the RBT G is 80.8 GPa and the uniformly distributed load 𝑞0 is set to and the analytical solution – 7 term 50000 N/m. 2 Based on the EBT, the governing equation of the problem is as given in equation (42). The boundary 0 conditions are given by; -2 EBT Analytical Solution 𝑑𝑤 TBT Analytical Solution 𝑥 = 0, 0 = 0 𝑎𝑛𝑑 𝑤0 = 0 𝑚 -4 RBT Analytical Solution 𝑑𝑥 𝑑2𝑤 𝑑3𝑤 -6 𝑥 = 𝐿, 02 = 0 𝑎𝑛𝑑 0 = 0 𝑑𝑥 𝑑𝑥3 -8 The analytical solution of this boundary value problem -10 based on the EBT is given by 𝑞 𝐿4 𝑥2 𝑥3 𝑥4 -12 𝐸( ) 0 0 0.5 1 1.5 2 𝑤0 𝑥 = (6 − 4 + ) (52) 24𝐷𝑥𝑥 𝐿2 𝐿3 𝐿4 Length Along Beam (m) Based on the TBT, the governing equations of the Fig. 8. Comparison of the analytical solutions in terms of problem are given in equation (44) and equation (45). The deflections obtained by the EBT, TBT and RBT 89 Deflection (mm) Deflection (mm) Deflection (mm) Deflection (mm) Maximum Deflection (mm) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 boundary conditions regarding to the TBT are given as Table 4. L2 error norm for different number of nodes based follows on EBT 𝑥 = 0, 𝜙 = 0 𝑎𝑛𝑑 𝑤0 = 0 𝑚 Meshless Number of Nodes 𝑑𝜙 𝑑𝑤 Method 21 Nodes 41 Nodes 161 Nodes 𝑥 = 𝐿, = 0 𝑎𝑛𝑑 𝜙 + 0 = 0 -8 -6 -6 𝑑𝑥 𝑑𝑥 SSPH 9.3439x10 5.7719x10 7.8041x10 The analytical solution of this boundary value problem based on the TBT is given by 0 𝑞 𝐿4 𝑥2 𝑥3𝑇 𝑥 4 𝑞 𝐿2 𝑥 𝑥2 𝑤0 (𝑥) = 0 (6 2 − 4 3 + 4) + 0 (2 − ) -5 (53) 24𝐷𝑥𝑥 𝐿 𝐿 𝐿 2𝜅𝑠𝐴𝑥𝑧 𝐿 𝐿 2 -10 Based on the RBT, the governing equations of the -15 problem are given in equation (47) and equation (48). The -20 boundary conditions regarding to the RBT are given as SSPH - 5 term - 21 Node - EBT follows -25 SSPH - 5 term - 41 Node - EBT SSPH - 5 term - 161 Node - EBT -30 𝑥 = 0, 𝜙 = 0 𝑎𝑛𝑑 𝑤 = 0 𝑚 Analytical Solution - EBT0 -35 𝑑𝜙 𝑑2𝑤 𝑑𝑤 𝑥 = 𝐿, ?̂?𝑥𝑥 − 𝛼𝐹 0 = 0, 𝑎𝑛𝑑 𝜙 + 0 = 0 𝑑𝑥 𝑥𝑥 𝑑𝑥2 𝑑𝑥 -40 0 0.5 1 1.5 2 Length Along Beam (m) The analytical solution of this boundary value problem based on the TBT is given by Fig. 12. Deflections of the beam computed based on the EBT and the analytical solution 𝑞 𝜇 ?̂? 𝑤 𝑅0 (𝑥) = 𝑤 𝐸 0 (𝑥) + ( 0 ) ( 𝑥𝑥2 ) (2𝐿𝑥 − 𝑥 2) + 2𝜆 𝐴𝑥𝑧𝐷𝑥𝑥 By using different numbers of nodes in the problem 𝑞 ( 0 𝜇 ?̂? ) ( 𝑥𝑥 ) [cosh 𝜆𝑥 + 𝜆𝐿 sinh 𝜆(𝐿 − 𝑥) − domain with 5 terms in TSEs expansion, the global L2 error 𝜆4 cosh 𝜆𝐿 𝐴𝑥𝑧𝐷𝑥𝑥 𝑞0𝜇 ?̂?𝑥𝑥 1+𝜆𝐿 sinh 𝜆𝐿 norms of the solutions obtained for the TBT are given in ( 4 ) ( ) ( )] (54) 𝜆 𝐴𝑥𝑧𝐷𝑥𝑥 cosh 𝜆𝐿 Table 5. It is clear in Table 5 that the SSPH method provides satisfactory numerical results and rate of convergence. It is The above boundary value problems are solved by using observed in Fig. 13 that the SSPH method agrees very well the SSPH method for different node distributions of 21, 41 with the analytical solution. and 161 equally spaced nodes in the domain x∈ [0,2]. The Revised Super Gauss Function given in equation (50) is used Table 5. Global L2 error norm for different number of nodes as the weight function. based on TBT For the numerical solutions, the radius of the support Meshless Number of Nodes domain (d) is chosen as 5 and the smoothing length (h) is Method 21 Nodes 41 Nodes 161 Nodes -8 -7 -8 chosen as 1.3∆. Also, for the numerical solutions based on SSPH 1.1353x10 3.2478x10 7.2764x10 the RBT, it is investigated the effect of the various numbers of terms employed in the TSEs when the number of nodes in The global L error norms of the solutions based on the the problem domain increases. The meshless parameters, d 2 RBT are given in Table 6 where different numbers of nodes and h, are selected to obtain the best accuracy. Computed are considered with varying number of terms in TSEs results by the SSPH method are compared with the analytical expansion. It is observed that the convergence rate of the solutions, and their rate of convergence and accuracy computed solution increases by increasing the degree of properties are investigated by using the global L2 error norm complete polynomials for 161 nodes in the problem domain. given in equation (51). In Table 4 the global L2 error norms of the solutions based on the EBT are given for different 0 numbers of nodes in the problem domain with 5 terms in -5 TSEs expansion. The similar case observed in the previous problem is also found in this problem. -10 -15 The accuracy of the SSPH method is not improved by increasing of the number of nodes in the problem domain. At -20 SSPH - 5 term - 21 Node - TBT least for the problem studied here, it is impossible to evaluate -25 SSPH - 5 term - 41 Node - TBT the convergence of the SSPH method because of the level of SSPH - 5 term - 161 Node - TBT -30 Analytical Solution - TBT the numerical errors which are too small obtained for -35 different number of nodes in the problem domain. The computed transverse deflection of the beam is virtually -40 0 0.5 1 1.5 2 indistinguishable from that for the analytical solution as seen Length Along Beam (m) from Fig. 12. Fig. 13. Deflections of the beam computed based on the TBT and the analytical solution. 90 Deflection (mm) Deflection (mm) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 Table 6. L2 error norm for different number of nodes with Fig. 16. Deflections of the beam based on the RBT along the varying number of terms in the TSEs x-axis computed by the SSPH method using different number of nodes and the analytical solution – 7 term Number of Number of Terms in the TSEs Nodes 5 Term 6 Term 7 Term The analytical solutions of the EBT, TBT and RBT are 21 1.7608 1.7608 1.7479 compared in Fig. 17. It is clear that the analytical solution 41 1.7783 1.7784 1.8504 obtained by the EBT is more close to the analytical solution 161 1.7920 1.7919 1.5278 obtained by the RBT than the TBT. At least for the problem studied here, the EBT yields more accurate results in terms of transverse deflection than the TBT. The convergence rate of the SSPH method is increasing as the number of nodes is increased in the problem domain 0 even by using same number of terms in the TSEs. It is clear -5 that the transverse displacement computed with the SSPH -10 method closer to the analytical solution of the problem given in Fig. 14 to Fig. 16. -15 -20 0 EBT Analytical Solution -25 -5 TBT Analytical Solution RBT Analytical Solution -10 -30 -15 -35 0 0.5 1 1.5 2 -20 SSPH - 5 term - 21 Node - RBT Length Along Beam (m) -25 SSPH - 5 term - 41 Node - RBT SSPH - 5 term - 161 Node - RBT Fig. 17. Comparison of the analytical solutions in terms of -30 Analytical Solution - RBT deflections obtained by the EBT, TBT and RBT (h/L=0.1) -35 It is observed that the accuracy of the numerical results -40 0 0.5 1 1.5 2 in terms of transverse deflection for TBT decrease with Length Along Beam (m) increasing h/L ratio. The h/L ratio is 0.1 in Fig. 17. It is Fig. 14. Deflections of the beam based on the RBT along the found that increasing of the h/L ratio is decreasing the x-axis computed by the SSPH method using different accuracy of the TBT in terms of transverse deflection as number of nodes and the analytical solution – 5 term shown in Fig. 18. -1 -10 0 -5 -10 0 -10 -15 -20 SSPH - 6 term - 21 Node - RBT EBT Analytical Solution -25 SSPH - 6 term - 41 Node - RBT 1 -10 TBT Analytical Solution SSPH - 6 term - 161 Node - RBT RBT Analytical Solution -30 Analytical Solution - RBT -35 2 -40 -10 0 0.5 1 1.5 2 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 h/L Ratio (m) Length Along Beam (m) Fig. 15. Deflections of the beam based on the RBT along the Fig. 18. Comparison of the analytical solutions in terms of x-axis computed by the SSPH method using different maximum deflections obtained with varying h/L ratio number of nodes and the analytical solution – 6 term 5. Conclusion 0 -5 The SSPH basis functions are employed to numerically solve the transverse deflections of the thick isotropic beams -10 subjected to different sets of boundary conditions and -15 uniformly distributed load by using strong formulation of the -20 problem. The numerical calculations are performed by using SSPH - 7 term - 21 Node - RBT -25 different number of nodes uniformly distributed in the SSPH - 7 term - 41 Node - RBT SSPH - 7 term - 161 Node - RBT problem domain and by employing different beam theories -30 Analytical Solution - RBT which are the EBT, TBT and RBT. The performance of the -35 SSPH method is investigated for the solution of the beam -40 problems with the TBT and RBT for the first time. It is found 0 0.5 1 1.5 2 Length Along Beam (m) that the SSPH method provides satisfactory results and 91 Deflection (mm) Deflection (mm) Deflection (mm) Deflection (mm) Maximum Deflection (mm) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 convergence rate for the studied problems here. It is observed [11] Giunta, G., Biscani, F., Bellouettar, S., Ferreira, A.J.M., that the computed results of transverse deflections agree very Carrera, E., Free vibration analysis of composite beams well with the analytical solutions. via refined theories, Composites Part B, 44, 540-552, 2013. For the problems studied, it is found that the accuracy of the computed results based on the TBT is deteriorated by the [12] [12] Arya, H., A new zig-zag model for laminated aspect ratio (h/L). 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(bayar@beun.edu.tr, alpadras@gmail.com) ‡ Corresponding Author; Gokhan Bayar, Department of Mechanical Engineering, Faculty of Engineering, Bulent Ecevit University, 67100 Zonguldak, Turkey, Tel: +90 3722574010/1224, Fax: +90 3722574023, email: bayar@beun.edu.tr Received: 06.06.2016 Accepted: 03.08.2016 Abstract-Lidar systems are one of the most important sensor infrastructures in autonomous vehicles and mobile robots. They are used for achieving indoor and outdoor mapping purposes. In the scope of this study, a new perspective to develop a lidar system is proposed. The system developed is constructed based on a low-cost infrared rangefinder sensor, low-cost slipring mechanism designed and manufactured, dc motor and microprocessor. The rangefinder sensor is mounted to a head-structure actuated by a dc motor that continuously rotates with a desired rotational velocity. The data coming from the rangefinder sensor flows through the microprocessor via the slipring. The design concept of the slipring mechanism gives an advantage that the data of the infrared rangefinder sensor can be taken while the sensor continuously rotates. The required power for the sensor can also be supplied by the slipring during motion. The decoding process of the data coming from the rangefinder sensor and motor control task are accomplished using an ATmega based microprocessor. A user interface is also created to communicate with the system and evaluate the performance of the whole structure developed. After conducting many experiments, successful results are obtained. The design steps of the system proposed and the experimental results are presented in this paper. Keywords Lidar, infrared sensor, slipring, laser scanner, range finder. 1. Introduction In the autonomous vehicle applications, path planning is one of the most critical issues that should be carefully Autonomous vehicles and mobile robots require designed. To achieve a successful path tracking control, recognizing their surroundings. They are generally reference path should be constructed by taking into programmed to track a predefined trajectory / path in order account the working environment structure, capabilities to perform an autonomous task. While they effort to track and capacities of the vehicle and sensors. Lidar systems a reference trajectory, a lidar system provides them the are one of the solutions for developing real-time maps of surrounding information (in order words lidar system the working area and planning the desired paths. They can behaves like their eyes). By this way, they can be able to be adapted into the path planning algorithms as a powerful recognize the obstacles, people, other vehicles, etc. The feedback option. The feedback information can also be use of information coming from a lidar system can provide used for the localization issues. An autonomous vehicle the opportunities to the autonomous systems to take some application, in which the location of the vehicle during the pre-actions so that any unexpected events could be motion should be known, requires real-time position and prevented. In addition to recognizing the working orientation information. This can also be achieved by the environment of the autonomous vehicles, lidar systems are use of a lidar system. An autonomous orchard application also used as a feedback sensor for the control systems. may be a good example for such a task (as presented in Desired trajectory tracking tasks including position, Fig. 1). In this figure, an orchard environment including orientation and velocity control routines can be supported trees and rows of trees and a four-wheeled vehicle is by the feedback information acquired from a lidar system. shown. In this scenario, the vehicle should drive itself autonomously inside the orchard. A lidar is mounted at the 94 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Gokhan Bayar et al., Vol.2, No.3, 2016 front-mid-center of the vehicle for recognizing the new approaches to develop lidar systems. The other topic surroundings. Its responsibilities are to provide the focuses on implementing the lidar systems into the robotic required data which is used for both detecting trees and applications. estimating rows of trees. The lidar data is also necessary In [1], a lidar application for agricultural tasks was for localizing the vehicle inside the orchard. Suppose that proposed. The data coming from a lidar was the only point (X0, Y0) is the starting position. The scanning radius sensor source that provides feedback information to the of the lidar is shown by R. In order to create a safe drive, mathematical model developed. In the scope of this study, let’s say this is an objective in this scenario, the vehicle a lidar canopy height model was developed using a semi- should move on the center line that is exactly the middle of automated pit filling algorithm. In [2], the accuracy two neighboring rows. When there is a positioning error, enhancement of large scale canopy heights was focused. A indicated by ye in Fig. 1, the lidar system should warn the new approach based on lidar output was. The system control system to take the required actions for steering the introduced was tested by the help of different scenarios. In vehicle through the desired path. This action is also [3], lidar system was used in city modeling and building depicted in Fig. 1. recognition tasks. The use of methodology introduced for building footprints was presented. Classification of the roof structures of the buildings was also evaluated using algorithm created based on the lidar sensor data. In [4], lidar sensor was used for a planetary application. A system based on the lidar sensor data was constructed for achieving autonomous safe landing on planetary bodies. In [5], a lidar system was developed for forestry applications. The methodology was constructed based on laser induced fluorescence imaging technique. The system developed was tested to observe the performance of the proposed structure. Working characteristics of the system was also produced. In [6], a lidar was used to estimate individual Fig. 1. The use of lidar in an autonomous orchard tree heights in forestry applications. The data coming form application lidar was accompanied with the aerial photography. In [7], a new approach for detecting stone monuments was The importance of the use of lidar systems in proposed. The method was constructed based on data autonomous applications is shown by a couple of examples coming from a lidar. In [8], a lidar system was developed presented above. Development of new lidar systems, for observing the atmospheric events and the particle approaches and models is still being continued. Parallel to density inside in it. In [9], a crop monitoring system was the enhancements in the lidar research area, a new proposed. The system was constructed based on a lidar and methodology for developing a lidar system is focused in 3D stereoscopic vision system. The system developed was this study. The new methodology involves the adaptation tested for autonomous agricultural applications. In [10], a of a low-cost infrared rangefinder and a low-cost and easy- lidar was placed on a mobile platform and the data was to-use slipring mechanism. The rangefinder sensor, which logged. The developed methodology used the data logged continuously rotates by the help of a head structure for extracting highway light poles and towers. In [11], an 0 designed, is used to scan the 360 surrounding of the lidar automatic classification of urban pavements system based system developed. This rotating mechanism enables that on lidar was built. In [12], a lidar based intelligent system the working environment of the sensor can be sensed. was developed for recognizing the ancient city walls. The Furthermore, when the sensor is surrounded by an object, modeling strategy was also was used for doing digital the 2D shape of the object can be detected. The rotational documentation. In [13], a road detection system was motion is provided using a dc motor. The slipring constructed using lidar point clouds. The system was mechanism is plugged to the system for achieving data modeled in a way that could have the capability for flow from the rangefinder sensor to the microprocessor. adapting itself according to the data intensity. In [14], a ATmega based microprocessor is also used to achieve lidar based system was built for detecting open water computation and communication purposes. surfaces in an Arctic delta. The system was modeled by This paper is organized as follows: the next section following the principles of decision tree classification presents the literature studies reviewed. Section 3 presents technique. the lidar systems and their working principles. Section 4 As seen in the literature studies, lidar systems are introduces the lidar system proposed in this study. Prior to commonly used in different applications ranging from the concluding remarks, experimental results are given in defense to industrial robotics, agriculture to automation, Section 5. unmanned ground vehicles to submarines, civil engineering to architecture. In the market, there are already 2. Literature Studies some lidar systems [15, 16, 17, 18] that are ready-to-use for the researchers and engineers. However, they may not The studies related to lidar systems can be reviewed be affordable for small-scale projects, small-scale research into two main topics. The first topic is about proposing companies, student works, startup formations, etc. Due to 95 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Gokhan Bayar et al., Vol.2, No.3, 2016 their high-prices, many lidar development research studies In this study, a design strategy to develop a lidar have been continuing. Their common goal is to build low- system is formed to meet the following criteria that the end price and easy-to-implement lidar systems. In parallel with product should be low-cost and accessible, easy-to-use and the recent developments in the lidar research, this study efficient. Following these design criteria, the lidar system aims to make a contribution to the continued investigations consisting of three main subsections is taken into about developing lidar systems and to create a new consideration. A low-cost infrared rangefinder sensor perspective for this field. (Sharp GP2Y0A21YK) that can be easily found in the market is used. The Lidar system developed is able to 3. Lidar Systems detect the objects that are closer than 80 cm. To trigger the sensor, 5V DC voltage is required. It gives analog voltage Lidar systems are commonly used in different research as the output which should be decoded using a studies and industrial applications. They are adapted into microprocessor. The block diagram of the system is shown the real-time running unmanned aerial and autonomous in Fig. 3. In this figure, the reference input and outputs, ground vehicles. Path planning, mapping and control data flows from sensors through the microprocessor and issues are supported by the data coming from lidar computer are shown. The control system constructed to systems. They are also used for terrestrial scanning. control the dc actuator is also presented in this block Topography map creation, mining reconstruction, diagram. architecture, archaeology, building researches and city reconstruction require environmental data supplied by a lidar. Lidar systems are also intensively used for observation of agricultural and forestry areas, urban sites, industrial and power plants. Real-time mapping of such regions can be created using the information provided by the lidar systems. The moving platforms like industrial forklifts, public transportation vehicles, trains, boats, off- road and unmanned vehicles are also suited with the lidar systems so as to ensure safe drive. In addition to providing fast drive and safe product handling, such systems are also utilized for increasing the reliability and performance in Fig. 3. Block diagram of the system developed manufacturing systems. They are also implemented to the tools and systems manufactured by the defense industries. The infrared rangefinder sensor is mounted to a The other usage area of the lidar systems is the marine designed head-structure that continuously rotates (Fig. 4). industry. Lidar systems can be plugged into any marine The rotation is provided using a 6V DC motor driven by a platforms to increase safe drive capabilities and working L298 H-bridge (motor motion control unit). The torque performance. Creating autonomy in marine products needs regulation is accomplished via a gear-head attached to the to be used lidar system as well. DC motor. An ATmega based microprocessor, called computing unit, is used for decoding, computing and A 2D lidar, laser scanning, system is depicted in Fig. communication purposes (Fig. 4). It needs 5V DC supply 2. The system consists of a light source, transmitter, voltage and is connected through the computer via USB. receiver and mirror. The light hitting the object and returning back is sensed by the receiver and the distance between the light source and the object is obtained. If an actuator is coupled to this system, a rotating lidar system would be built. Fig. 2. Working principle of a lidar (laser scanning) system (left). Using an actuator to develop a rotating-lidar system (right) Fig. 4. General view of the lidar system developed in this study. Computing unit consists of an ATmega based 4. Lidar System Developed in This Study microprocessor 96 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Gokhan Bayar et al., Vol.2, No.3, 2016 To get the rotation information, a simple encoder unit presented in Fig. 5 is also built. This unit consists of an encoder disc and Omron photomicrosensor [19]. The resolution of the encoder unit is 36 pulses per revolution. The counting of the pulses is also achieved using the ATmega based computing unit. Fig. 6. Slipring mechanism developed. Top view (left) and side view (right) are shown. 5. Experimental Studies In order to see the performance and accuracy of the lidar system proposed, the sensor structure introduced above is experimentally tested. It is placed at the center of a box which has the dimensions of 30 cm x 21 cm. The Fig. 5. Encoder unit including an encoder disc and first experiment is performed for only 1 complete photomicrosensor revolution. The resolution of the lidar system developed is 10 degrees therefore 36 distance measurements are In order to achieve data flow from the infrared obtained for one revolution. The results for this scenario rangefinder sensor, which continuously rotates during are presented in Fig. 7 (top-left). To see the performance operation, to the computing unit, a new design perspective and accuracy enhancement while the number of turns is for slipring mechanism is considered. The top and side increased, experiments are performed from one to ten views of the developed system are shown in Fig. 6. The complete revolutions. The results obtained for “i” infrared rangefinder sensor needs three cable connections; revolution(s), (i = 1, 2, …,9), are shown in Fig. 7. one is for data flow and the other two is for power supply. The simple slipring mechanism, presented in Fig. 6, is The experiment results including 10 full revolutions constructed to make these connections. The data flow is are given in Fig. 8. The results are presented in polar plots. achieved using the inner circle and the power is supplied The left polar plot shows all the measurements of the 10 via the middle and the outer circles (Fig. 6-left). turns whereas the right polar plot presents the average values of each measurement. Fig. 7. Experiments performed using the lidar system. The results including 1 to 9 complete revolutions are presented 97 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Gokhan Bayar et al., Vol.2, No.3, 2016 6. Analysis and Conclusion In indoor and outdoor mapping applications used for autonomous drives and automations, one of the important sensorial systems is the lidar. They are adapted into the control systems for providing feedback information. Lidar systems are able to scan the surrounding from 0 to 360 degrees in variety of distances. The distances may range from 0 to a few kilometers. In the market, there are already some lidar systems that are used for autonomous research and applications. However, these products may not be accessible by the small companies, small research groups Fig. 8. Experiment results including 10 full revolutions. and students because of their high-cost. In the scope of this The left polar plot shows the measurement for all turns. study, it is objected to develop a low-cost, easy-to-use and The right polar plot indicates the average values of the easy-to-implement lidar system. The system proposed is measurements built using a low-cost infrared rangefinder sensor and a slipring mechanism designed. The end product is able to The results given in Fig. 8 and 9 show that increasing rotate continuously and give distance data in every 10 the number of scans increases the accuracy and degrees. The rotation is provided via a dc motor and the performance. The box’s shape can be poorly estimated if rotation information is obtained using an encoder. An only 1 revolution is performed (Fig. 9-a) whereas the ATmega based microprocessor is also used as the shape obtained by the 10 complete revolutions is able to computational unit of the lidar system. In order to see the give almost the actual shape of the box (Fig. 9-b). These accuracy and the performance of the system proposed, a results emphasize that a lidar system developed using a user interface is created in the computer side. Many low-cost infrared rangefinder sensor, a rotating head- experiments are performed and successful results are structure and a simple slipring mechanism can be obtained. The results obtained in this study emphasize that successfully used for scanning and recognizing purposes. the design strategy introduced provides a new perspective for developing lidar systems and can be used for the Estimated 15 Actual further researches. 10 References 5 [1] J. R. Ben-Arie, G. J.Hay, R. P. Powers, G. Castilla, 0 B. St-Onge, Development of a pit filling algorithm for LiDAR canopy height models, Computers & -5 Geosciences, Vol. 35, pp. 1940–1949, 2009. -10 [2] M. Hollaus, W. Wagner, C. Eberhöfer, W. 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The measurements of 1 revolution (a) and 10 characteristics of laser-induced fuorescence imaging revolutions (b). The red-colored-lines indicate the actual lidar for forestry applications, Forest Ecology and box’s shape that has the dimensions of 30 cm x 21 cm. The Management, Vol. 128, pp. 129-137, 2000. blue-colored-lines indicate the experimental results 98 Y-Direction (cm) Y-Direction (cm) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Gokhan Bayar et al., Vol.2, No.3, 2016 [6] J. C. Suarez, C. Ontiveros, S. Smith, S. Snape, Use of descriptors, Construction and Building Materials, airborne LiDAR andaerial photography in the Vol. 102, pp. 208–215, 2016. estimation of individual tree heights in forestry, [12] L. Cheng, Y. Wang, Y. Chen, M. Li, Using LiDAR Computers & Geosciences, Vol. 31, pp. 253–262, for digital documentation of ancient city walls, 2005. Journal of Cultural Heritage, Vol. 17, pp. 188–193, [7] G. Cecchi, L. Pantani, V. Raimondi, L. Tomaselli, G. 2016. Lamenti, P. 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Puente, Automatic classification of urban [19] https://www.omron.com/ecb/products/photo/#photo pavements using mobile LiDAR data and roughness micro, Last accessed, June 05, 2016. 99 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Vedat Karaman et al., Vol.2, No.3, 2016 Calculation and Optimizing of Brake Thermal Efficiency of Diesel Engines Based on Theoretical Diesel Cycle Parameters * ** * * Safak Yildizhan , Vedat Karaman ‡, Mustafa Ozcanli , Hasan Serin *Department of Automotive Engineering, Cukurova University, 01330 Adana, Turkey. **Department of Mechanical Engineering, Istanbul Gelisim University, 34315 Istanbul, Turkey. (yildizhans@cu.edu.tr, vkaraman@gelisim.edu.tr, ozcanli@cu.edu.tr, hserin@cu.edu.tr) ‡ Corresponding Author: Vedat Karaman, Department of Mechanical Engineering, Istanbul Gelisim University, 34315 Istanbul, Turkey, Tel:+90 212 422700, Fax: +90 2124227401, vkaraman@gelisim.edu.tr Received: 25.07.2016 Accepted: 02.09.2016 Abstract-In this study, a theoretical study has been evaluated in order to calculate and optimize diesel engine brake thermal efficiency values. In the study three main parameters which are compression ratio, ratio of specific heat and cut-off ratio, based on ideal diesel cycle were evaluated. Compression ratio, ratio of specific heats and cut-off ratios were chosen between the interval of; 12:1-24:1, 1,2-1,4 and 1,5-3,0, respectively. Theoretical study showed that compression ratio significantly affects the engine characteristics that calculated in this study. Experiments revealed that the higher compression ratio results with higher brake thermal efficiency (BTHE) and thus lower specific fuel consumption (SFC). The calculation study showed that increasing cut-off ratio caused to decrease of brake thermal efficiency. Also, study revealed that increment of ratio of specific heats improved brake thermal efficiency. Keywords Thermal efficiency, performance, compression ratio, specific heats, cut-off ratio, optimization. 1. Introduction the effects of these parameters mostly using variable compression engine (VCR) [2-8]. A large part of the energy consumed in the world is The diesel engines are very fuel efficient and thus derived from fossil fuels such as petroleum, coal and natural provide fuel economy. The operational simplicity of diesel gas. But, these petroleum based non-renewable resources engines makes diesel engines more preferable in the will come to an end in the short run. Therefore, the transportation sector and agricultural and forestry machinery. investigations for renewable and sustainable alternative The extinction risk of fossil fuel and high cost of the energy sources which can provide the necessary energy petroleum causes to increase of effort in the means of demand of the world has gained attention all over the world alternative fuel development. [9]. due to hazard of depletion of fuels, high price of petroleum and environmental concerns such as air pollution and global After the oil crisis of the 1970s, investigation efforts on warming [1]. In the last decades, research interests on the the field of the internal combustion engines have been internal combustion engines (ICE) have been explored in the extended in the area of alternative fuels, which are available area of alternate fuels, which are renewable, locally locally, biodegradable, less toxic, environment friendly available, environment friendly [2]. Beside these fuel renewable, compared to fossil fuels [10]. Also, beside fuel researches the operating conditions of engines have gained researches many scientists have been working on engine very importance by researchers and manufacturers. parameters such as compression ratio and injection timing. Improvement internal combustion engines by optimizing the These main parameters of engines effect directly all operating conditions have been one of the primary study performance and emission characteristics of ICE. Thus, subjects through researchers. To be able to increase the many researchers have investigated the effects of these efficiency of an engine all effects of engine parameters parameters mostly using variable compression engine should be known. Thus, many researchers have investigated (VCR). 100 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Vedat Karaman et al., Vol.2, No.3, 2016 Jindal et al. [3] reported a study which investigates the (compression ignition) engines are mostly used for effects of the engine design parameters such as compression heavy-duty vehicles, trucks, buses, etc. which require a ratio (CR) and fuel injection pressure on the performance of very high amount of torque. the engine. The author studied the subject with some critical  Intake stroke: The piston starts to move downward from performance criterias such as brake thermal efficiency, the top dead center to bottom dead center, the intake specific fuel consumption, and emissions of carbon valve opens, and this movement lets the introducing the monoxide, carbon dioxide, hydrocarbons, nitrogen oxides air charge inside the cylinder. and smoke opacity with Jatropha methyl ester as fuel. Depnath et al. [11] presented a study that investigates the  Compression stroke: The piston moves back to top dead variable compression ratio diesel engine when the engine is center from bottom dead center and compresses the air fueled with palm oil methyl ester thermodynamically. The inside the cylinder and the temperature inside cylinder effect of compression ratio (CR) and injection timing (IT) on rises over the auto-ignition temperature of the fuel. energy and energy potential of a palm oil methly ester  Combustion stroke (power stroke) : At the end of the (POME) was found by them. The test were performed in a compression stroke (before the piston reaches the top single cylinder, direct injection, water cooled variable dead center) the injectors start to inject fuel inside to compression ratio diesel engine at a constant peed of 1500 cylinder. After the ignition delay period the fuel is rpm under a full load. Amarnath and Prabhakaran [10] spontaneously auto-ignites. The fuel-air mixture combust reported a study which is related with the thermal produce a pressure on the cylinder head and pushes the performance and emissions of a variable compression ratio cylinder downward which is the main object of the diesel engine fueled with karanja biodiesel and optimized the engine. parameters based on experimental datas. Al Dawody and Bhatti[12] investigated the emission, performance and the  Exhaust stroke: After the piston hits the bottom of combustion, characteristics of a diesel engine fueled with cylinder (bottom dead center) ,the piston start to move soybean biodiesel-diesel blends experimentally and upward and the exhaust valve opens because between the computationally. cylinder and exhaust manifold pressure is different, and the sweep effect of the piston make the exhaust gases In this study, a theoretical calculation were evaluated leave the cylinder to go out through the tail pipe. based on ideal diesel cycle by using parameters of compression ratio, ratio of specific heats, and cut-off ratio in The four steps of ideal diesel combustion ; order to optimize the operational conditions of a diesel engine. Theoretical calculations in this study shows the 1-2 isentropic compression effects of engine operating parameters which is important to 2-3 constant pressure heat addition have guess before performing time consuming and costly experiments. 3-4 isentropic expansion 4-1 constant volume heat rejection 2. Material Method 2.1. Calculation Method The most crucial characteristic of diesel engine is its fuel economy, which can excel up to 40% in vehicle applications and even up to 50% in two-stroke units of marine exciting or generators. As a consequence, vehicles running with compression ignition engines have lower specific fuel consumption and reduced carbon dioxide emissions comparing to its counterpart spark ignition engines. Moreover, diesel engines are less sensitive in terms of air– fuel ratio variations, in peak cylinder pressures and temperatures absence of throttling, high torque and high tolerability make diesel engines more preferred. Compression ignition engines are assumed to operate Fig 1.a.b P-V and T-S diagrams of idealized diesel cycle with the principle of ideal cycle. Actual working cycle of Underlining that the ideal diesel cycle is operated in a diesel cycle is significantly different from ideal cycles. Yet, closed system, and air-standard assumptions were made for to be able to study parametrically actual cycles are idealized working fluid (air). Variations of potential and kinetic with some assumptions. energies are insignificant. During the two isentropic Ideal Diesel Cycle processes no heat transfer is involved. The energy balances processes are:  In compression-ignition engines, air is compressed to above the auto ignition temperature of the fuel. After the -w12 = u2 - u1 (1) injection of fuel spray the combustion occurs with a delay -w34 = u4 - u3 (2) time (ignition delay, a few crack angles). Diesel 101 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Vedat Karaman et al., Vol.2, No.3, 2016 w12 is negative because of the compression and w34 is positive because of the expansion process which air does the ηth(%) = (6.6) work. Constant pressure heat addition process, w23 = P2(v3 - v2) (3) Where; The energy balances: is thermal efficiency, q23 = u3 - u2 + w23 = h3 - h2 (3.1) α is the cut-off ratio (ratio between the end and start volume Since there is no change in the volume there is no work in for the combustion phase), the heat rejection process. The energy balance; cp is specific heat at constant pressure, q41 = u1 - u4 (4) cv is specific heat at constant volume, Since the heat is added to the system q23 is positive and since the heat is rejected during the process q is negative. γ is ratio of specific heats (cp/cv), 41 For the full cycle, r is the compression ratio. q + q - w - w = 0 (5) Theoretical equation shows that thermal efficiency of the 23 41 12 34 diesel cycle depends on three parameter which are; Brake thermal efficiency (ηth): A gauge of overall engine compression ratio (r), ratio of specific heats (γ) and cut-off efficiency is given by the brake thermal efficiency. Brake ratio of the cycle ( . thermal efficiency is the ratio of energy in the brake power to the fuel energy. Figure A shows the entropy (S) , pressure (P) 3. Results and Discussion and volume (V) diagrams of idealized diesel cycle. Thermodynamically; In this study, a theoretical calculation of brake thermal ( efficiency (BTHE) was evaluated analytically. Three main Wcycle = (6) parameters that effect the thermal efficiency calculation of ideal diesel cycle were studied. Compression ratio which is Q2-3 = Q4-1 = the main parameter that determines the theoretical BTHE value was varied between the range of 12:1 and 24:1. Ratio Q2-3 = cp(T3-T2) Q4-1 = -cv(T1-T4) = cv(T4-T1) of specific heats (γ) and cut-off ratios ( ) were chosen between the rage of 1,2-1,4 and 1,5-3,00, respectively. γ = (6.1) Figures (1-5) shows the BTHE values of for different compression ratios, cut-off ratios and specific heat ratios. The analyses revealed that, CR increment significantly increases BTHE values. For all cut-off ratios and specific heat ratios maximum BTHE values were obtained with 24:1 Since 1-2 adiabatic compression ratio value. Increasing specific heats (γ) values further increased BTHE values. But, increasing cut-off ratio (6.2) ( ) values caused a significant decrement in the means of Since 2-3 constant pressure BTHE values. According to calculation results, the best efficiency of thermal study was obtained with 1,4 specific heat ratio, 1,5 cut-off ratio and 24:1 CR. (6.3) ( 6 . 4 ) Fig. 1. The change in thermal efficiency according to (ηth) = BrakePower/Fuel Energy (6.5) different compression and cut off ratio in cases where ratio of specific heats (γ) is 1.2 constant 102 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Vedat Karaman et al., Vol.2, No.3, 2016 Fig. 2. The change in thermal efficiency according to Fig. 5. The change in thermal efficiency according to different compression and cut off ratio in cases where ratio of different compression and cut off ratio in cases where ratio of specific heats (γ) is 1.25 constant specific heat (γ) is 1.4 constant Fig. 3. The change in thermal efficiency according to Fig. 6. The change in thermal efficiency according to different compression and cut off ratio in cases where ratio of different specific heats ratio and cut off ratio in cases where specific heats (γ) is 1.3 constant compression ratio is 18 constant The calculation study showed that BTHE values can be obtained as up to 68%. But this value is not realistic for actual applications since this study was evaluated with the formula of ideal diesel cycle. Idealization of actual diesel cyle includes many assumptions and thus there are tremendous differences between calculation datas and experimental datas. Hariram and Shangar published an article that researchs the effects of the compression ratio on combustion characteristics of a compression igntion engine [13]. The authors studied with three different compression ratios (16:1, 17:1, and 18:1). The authors reported that increasing CR resulted with higher BTHE values and thus lower brake specific fuel consumption. The author reported that increasing compression ratio from 16:1 to 18:1 improved BTHE value up to 13% at full load conditions which is coincidence with the calculation datas obtained in this study. Fig. 4. The change in thermal efficiency according to In another study V. Gnanamoorthi and G. different compression and cut off ratio in cases where ratio of Devaradjaneto found the maximum possible and optimum specific heats (γ) is 1.35 constant replacement of diesel fuel by ethanol and compare the performance of diesel engine fuel led with ethanol-diesel 103 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Vedat Karaman et al., Vol.2, No.3, 2016 blend for various compression ratios (17.5:11, 18.5:1, 19.5:1) [6] Hoeltgebaum, T., Simoni, R., Martins, D., and study the effect of compression ratio and using the best “Reconfigurability of engines: A kinematic approach to emulsified technique to achieve acceptable range of variable compression ratio engine. “Mechanism and Machine efficiency up to E40.[14] Theory, vol.96, pp. 308-22, 2016. As it is shown in the experimental studies, increasing the [7] Serin H., M. Ozcanli, M.K. Gokce., G. Tuccar compression ratio improves the efficiency of the engine. [2- “Biodiesel Production From Tea Seed (Camellia Sinensis) 5] In this study it was found a similar results that obtained in Oil and its Blends With Diesel Fuel.” International Journal of the previous studies. Green Energy, vol.10:4, pp.370-7., 2013. [8] Yildizhan, S., Yasar, A., “Performance and Emission 3. Conclusions Characteristics of Diesel Engine Operating on Biodiesel and Biodiesel Blended with Methanol and Propanol.”  A theoretical study was evaluated with three parameters International Journal of Scientific and Technological that effect the brake thermal efficiency of ideal diesel Research, Vol 1, No.1, pp.270-8 2015. cyle. [9] Ramadhas A.S., Muraleedharan C., and Jayaraj, S.,  The parametrical study showed that increasing “Performance and Emission Evaluation of a Diesel Engine compression ratio significantly improves the brake Fueled with Methyl Esters of Rubber Seed Oil”, Renewable thermal efficiency. Energy vol. 30,pp. 1789-1800,2005.  The analyses revealed that, increasing ratio of specific [10] Amarnath, H.K., and Prabhakaran P., “A Study on the heat further improves the brake thermal efficiency. But, Thermal Performance and Emissions of a Variable increasing cut-off ratio resulted with lower brake thermal Compression Ratio Diesel Engine Fuelled with Karanja efficiency. Biodiesel and the Optimization of Parameters Based on  Although, the calculation results were significantly Experimental Data. “International Journal of Green Energy, different from the actual values, the trend of brake vol.9:8, pp.841-863, 2012. thermal efficiency with different parameters was [11] Depnath, B.K., Sahoo, N., and Saha, U.K., compatible with actual processes. “Thermodynamic analysis of a variable compression ratio diesel engine running with palm oil methyl ester. “ Energy  The calculations showed the effects of different operating running with palm oil methyl ester. Energy Conversion and parameters of the diesel engine based on ideal diesel Management vol.65, pp.147-154. 2012. cycle which can be used to optimize the operating [12] Al Dawody, M.F., and Bhatti, S.K., “Experimental and conditions of a diesel engine. computational ınvestigations for combustion, performance and emission parameters of a diesel engine fueled with References soybean biodiesel-diesel blends. “ Energy Procedia, biodiesel-diesel blends. vol.52,pp. 421-430,2014. [1] Demirbas A. “Biodiesel production from vegetable oils [13] Hariram, V., and Shangar, R.V., ‚‘‘Influence of via catalytic and non-catalytic supercritical methanol compression ratio on combustion and performance transesterification methods.” Progress in Energy and characteristics of direct injection compression ignition Combustion Science vol.31,pp.466–87,2005 engine.“Alexandria Engineering Journal, vol.54:4, pp.807- [2] Amarnath, H.K., Prabhakaran, P., “A Study on the 81,2015. Thermal Performance and Emissions of a Variable [14] V. Gnanamoorthi , G. Devaradjane “Effect of Compression Ratio Diesel Engine Fuelled with Karanja compression ratio on the performance, combustion and Biodiesel and the Optimization of Parameters Based on emission of DI diesel engine fueled with ethanol e Diesel Experimental Data. “International Journal of Green Energy, blend.” Journal of the Energy Institute,vol.88,pp.19-26,2015. vol.9:8, pp.841-863,2012. [3] Jindal S, Nandwana B.P., Rathore N.S., Vashistha V., “Experimental investigation of the effect of compression ratio and injection pressure in a direct injection diesel engine running on Jatropha methyl ester.” Applied Thermal Engineering, vol.30,pp. 442-8, 2010. [4] Mohanraj, T., Murugu Mohan Kumar, K., “Operating Characteristics Of A Variable Compression Ratio Engine Using Esterified Tamanu Oil.” International Journal of Green Energy, vol.10:3,pp. 285-301, 2013. [5] Muralidharan,K., Vasudevan, D., “Performance, emission and combustion characteristics of a variable compression ratio engine using methyl esters of waste cooking oil and diesel blends.” Applied Energy, vol.88, pp. 3959-68, 2011. 104 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics Armagan Karamanli* *Department of Mechatronics Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, 34215 Istanbul, Turkey. (afkaramanli@gelisim.edu.tr) ‡ Corresponding Author; Armagan Karamanli, Department of Mechatronics Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, 34215 Istanbul, Turkey, Tel: +90 2124227020, armagan_k@yahoo.com Received: 28.07.2016 Accepted: 02.09.2016 Abstract-The elastostatic deformations of functionally graded beams under various boundary conditions are investigated by using different beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The numerical calculations are performed based on the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories. The performance of the SSPH method is investigated for the comparison of the different beam theories where the beams are composed of two different materials for the first time. For the numerical results various numbers of nodes are used in the problem domain. Regarding to the computed results for Reddy-Bickford beam theory various numbers of terms in the Taylor Series Expansions (TSEs) are employed to improve the accuracy. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections are carried out with the analytical solutions by using the global L2 error norm. Keywords Meshless method, functionally graded beam, bending deflection, SSPH method, shear deformation theories. 1. Introduction The engineering applications where the FGMs may be used are the aerospace, biomedical, defence, energy, One of the biggest problems that the engineers face with optoelectronics, automotive (engine components), turbine during the new product development process is the selecting blade, reactor components (nuclear energy) and etc. FGMs of the proper material to be used for the engineering may be used in different application areas with the applications. There are many factors to be considered for the development of new fabrication technologies, the reduction optimization of the selection process such as the cost of raw in cost of production, improvement in the properties of material and production, fabrication techniques, logistics, FGMs. material properties, requirements of customers with severe The advantages of the FGMs over the conventional and operating conditions for instance; the material should be hard classical composite materials are basically due to varying but also ductile or the material can withstand very high material properties over a changing dimension which allows surface temperature of 2000K and a temperature gradient of enhancing the bond strength through the layer interfaces, 1000K across a 10 mm thickness and so on. In 1984, a group high resistance to temperature shocks, lower transverse shear of Japanese scientists working on a space shuttle project stresses, etc. Researchers have been devoted a considerable requiring a thermal barrier with high performance properties number of studies to predict and to understand the mechanics introduced a novel material called Functionally Graded of the FGM structures. Material (FGM). FGMs can be classified as advanced materials which are inhomogeneous and made up of two (or An elasticity solution of a FGM beam subjected to more) different materials combined in solid states with transverse loads based on the Euler Bernoulli Beam Theory varying properties as the dimension changes. (EBT) is given in [1]. By using the semi inverse method, a closed form 2D plane elasticity solution of a cantilever beam 105 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 with different loading conditions and gradation laws can be Meshless methods are the most promising and have found in [2]. In [3], the analytical solution of a 2D plane attracted considerable attention for the analysis of stress problem for a Functionally Graded Beam (FGB) engineering problems with intrinsic complexity. Meshless subjected to normal and shear tractions of arbitrary form on methods are widely used in static and dynamic analyses of the top and bottom surfaces and under various end boundary the isotropic, laminated composite and FGM beam problems conditions is presented. The bending solutions of the [35-41]. To obtain the approximate solution of the problem generally anisotropic beams with elastic compliance by a meshless method, the selection of the basis functions is parameters being arbitrary functions of the thickness almost the most important issue. The accuracy of the coordinate are investigated in [4]. The static behaviour of computed solution can be increased by employing different FGBs under ambient temperature by using the higher order number of terms in TSE or increasing number of nodes in the beam theory is studied extensively in [5] for the transverse problem domain or by increasing the degree of complete displacements, axial stress and transverse shear stress polynomials. Many meshless methods have been proposed distribution. The static and dynamic behaviours of by researchers to obtain the approximate solution of the functionally graded Timoshenko and Euler–Bernoulli beams problem. The Smoothed Particle Hydrodynamics (SPH) are investigated by introducing a new function which helps method is proposed by Lucy [42] to the testing of the fission to decouple the governing equations and allows representing hypothesis. However, this method has two important the transverse deflection and rotational angle only in the shortcomings, lack of accuracy on the boundaries and the terms of this new function [6]. The static response of tensile instability. To remove these shortcomings, many functionally graded material short beam is studied in [7] meshless methods have been proposed by several researchers using the parabolic shear deformation theory and sinusoidal [43-63]. shear deformation theory to show the ability of higher order The main scope of this work is to evaluate the theories to enhance predictions provided by classical beam performance of the SSPH method employing the strong theories. The flexional bending of a simply supported FGB is formulation for the static transverse deflection analysis of the studied by using different higher order beam theories with FGBs based on various beam theories such as EBT, TBT and varying gradation laws [8]. The refined beam theories are the Reddy – Bickford Beam Theory (RBT). To provide a fair introduced for the static analysis of the FGBs whose and comparable evaluation, two FGB problems of which properties are graded along one or two directions in [9]. The analytical solutions are available in the literature will be used determination of the shear correction factor is investigated in for the numerical calculations. [10] for various gradation laws. The static bending solutions of the FGM Timoshenko Beams are obtained analytically in Based on the above discussions, the main novelty of this terms of the homogeneous Euler Bernoulli beams by using work is that there is no reported work on the bending mathematical similarity and load equivalence between the deflections of the functionally graded beams subjected to the governing equations [11]. The static behaviour of the FGBs different boundary conditions by using the SSPH method. are also studied by using the quasi-3D theory to show the Since the basis functions and the derivatives of these effects of shear deformation and thickness stretching on the functions are obtained simultaneously and the usage of a displacement and stresses [12]. Several refined beam finite constant weight function is possible to obtain the elements obtained by means of the Carrera Unified approximate solution, the SSPH method has an advantage Formulation (CUF) are used to static analysis of the FGBs over the Moving Least Squares, Reproducing Kernel Particle [13]. In 14, the combination of the Timoshenko Beam Method, Modified Smoothed Particle Hydrodynamics and Theory (TBT) and the finite volume method is developed for the Strong Form Meshless Implementation of Taylor Series the static and the free vibration of the FGBs. Due to the Method [51-56]. different implementation areas of the FGMs in engineering In section 2, the formulation of the basis function of the applications, free and forced vibration [15-26] and buckling SSPH method is given. In section 2, the homogenization of behaviour [27-34] of the functionally graded structures have material properties of the FGB is presented. The formulation been extensively investigated by several researchers. of the EBT, TBT and RBT based on the FGM and the SSPH As it is seen form above discussions, the studies related method are given in Section 4. In Section 5, numerical to analytical and semi-analytical solutions of these initial and results are given based on the two FGB problems which are a boundary value problems which have complex governing simply supported FGB under uniformly distributed load and equations are very limited in the literature. Therefore, one a cantilever FGB under the uniformly distributed load. The may easily show that the numerical methods such as finite performance of the SSPH method is evaluated by using the element methods (FEM), meshless methods, GDQM, etc. are analytical solutions of studied problems. widely used and have shown great progress for the analysis of these complex problems. However, for convenience and 2. Formulation of Symmetric Smoothed Particle generality considerations at least to the best of the author’s Hydrodynamics knowledge, there is no common agreement and also no reported work regarding to the meshless methods of which Taylor Series Expansion (TSE) of a scalar function for best fit in terms of accuracy, CPU time, flexibility for 1D case can be given by dealing with the complex geometries, extendibility to multi- 1 𝑑 𝑚 dimensional problems and etc., for the static and dynamic 𝑓(𝜉) = ∑𝑛𝑚=0 [(𝜉 − 𝑥) ] 𝑓(𝑥) (1) 𝑚! 𝑑𝑥 analysis of the FGBs based on the different beam theories. 106 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 where 𝑓(𝜉) is the value of the function at 𝜉 located in near of 𝑑3𝑓(𝑥) = 3! 𝑄4(𝑥) = ∑ 𝑀 3 𝐽=1 𝐾4𝐽𝐹𝐽 x. If the zeroth to sixth order terms are employed and the 𝑑𝑥 higher order terms are neglected, the equation (1) can be 𝑑4𝑓(𝑥) = 4! 𝑄5(𝑥) = ∑ 𝑀 4 𝐽=1 𝐾5𝐽𝐹𝐽 written as follows, 𝑑𝑥 5 𝑓(𝜉) ( ) = 𝑃(𝜉, 𝑥)𝑄(𝑥) 𝑑 𝑓 𝑥 (2) = 5! 𝑄 (𝑥) = ∑𝑀 𝑑𝑥5 6 𝐽=1 𝐾6𝐽𝐹𝐽 6 where 𝑑 𝑓(𝑥) 6 = 6! 𝑄7(𝑥) = ∑ 𝑀 𝐽=1 𝐾7𝐽𝐹𝐽 (9) 𝑑𝑥 ( ) 2 ( ) 𝑇𝑑𝑓 𝑥 1 𝑑 𝑓 𝑥 1 𝑑6𝑓(𝑥) 𝑄(𝑥) = [𝑓(𝑥), , , … , ] (3) The formulation of the SSPH method can be found in 𝑑𝑥1 2! 𝑑𝑥 2 1 6! 𝑑𝑥 6 1 [52-57]. 𝑃(𝜉, 𝑥) = [1, (𝜉1 − 𝑥1), (𝜉1 − 𝑥 2 6 1) , … , (𝜉1 − 𝑥1) ] (4) 3. Homogenization of Material Properties To determine the unknown variables given in the Q(x), both T We assume that the beam of length L, width b, thickness sides of equation (2) are multiplied with W(𝜉, x)P(𝜉, x) and h is made of two randomly distributed different isotropic evaluated for every node in the CSD. In the global constituents. Further, the macroscopic response of the FGB numbering system, let the particle number of the kth particle is isotropic and the material parameters vary only in z in the compact support of W(𝜉, x) be r ( k ). The following direction as shown in Fig. 2. The rule of mixture is used to equation is obtained find the effective material properties at a point. According to ∑𝑁(𝑥) 𝑟(𝑘) 𝑟(𝑘) 𝑟(𝑘) 𝑇 the rule of mixtures, the effective material properties of the 𝑘=1 𝑓(𝜉 ) 𝑊(𝜉 , 𝑥)𝑃(𝜉 , 𝑥) beam, Young’s modulus E and shear modulus G can be 𝑇 = ∑ 𝑁(𝑥) 𝑘=1 [𝑃(𝜉 𝑟(𝑘), 𝑥) 𝑊(𝜉𝑟(𝑘), 𝑥)𝑃(𝜉𝑟(𝑘), 𝑥)] 𝑄(𝑥) (5) given by where N(x) is the number nodes in the compact support domain (CSD) of the W(𝜉,x) as shown in Fig.1. Compact Support Domain 𝒙 Fig. 2. Geometry of the FGB composed of two isotropic 𝒊 constituents 𝐸(𝑧) = 𝐸1𝑉1(𝑧) + 𝐸2𝑉2(𝑧) 𝒙𝒈 𝐺(𝑧) = 𝐺1𝑉1(𝑧) + 𝐺2𝑉2(𝑧) (10) where 𝐸1, 𝐸2, 𝐺1 and 𝐺2 are the material properties of two constituents, 𝑉1 and 𝑉2 are volüme fractions of the Fig. 1. Compact support of the weight function W(ξ, x) for constituents. The relation of the volume fractions can be the node located at x = (xi, yi) expressed as follows; Then, equation (5) can be given by 𝑉1(𝑧) + 𝑉2(𝑧) = 1 (11) 𝐶(𝜉, 𝑥)𝑄(𝑥) = 𝐷(𝜉, 𝑥)𝐹(𝑥)(𝜉, 𝑥) (6) According to the power law form, the volume fraction of where C(𝜉, x) = P(𝜉, x)TW(𝜉, x)P(𝜉, x) and D(ξ, x) = the constitute 1 can be given by P(ξ, x)T W(ξ, x). 1 𝑧 𝑝 𝑉1(𝑧) = ( + ) (12) 2 ℎ The solution of equation (6) is given by where p is the gradation exponent which determines the 𝑄(𝑥) = 𝐾(𝜉, 𝑥)𝐹(𝜉) (7) material property through thickness of the beam. At the where K(x)(𝜉, x) = C(𝜉, x)−1D(𝜉, x). Equation (7) can be bottom surface of the beam, the volume fraction of the also written as follows constitute 1 is zero, 𝑉1 = 0. At the top surface it is found as 𝑉1 = 1. The effective material properties can be found by 𝑄𝐼(𝑥) = ∑ 𝑀 𝐽=1 𝐾𝐼𝐽𝐹𝐽 , 𝐼 = 1,2, … ,6 (8) using the equations (10), (11) and (12) as follows Where M is the number of nodes and F J 𝑝J = f(𝜉 ). Seven 1 𝑧𝐸(𝑧) = (𝐸1 − 𝐸2) ( + ) + 𝐸2 components of equation (8) for 1D case are can be written as 2 ℎ 1 𝑧 𝑝 𝑓(𝑥) = 𝑄1(𝑥) = ∑ 𝑀 𝐽=1 𝐾1𝐽𝐹𝐽 𝐺(𝑧) = (𝐺1 − 𝐺2) ( + ) + 𝐺2 (13) 2 ℎ 𝑑𝑓(𝑥) = 𝑄 (𝑥) = ∑𝑀 𝐾 𝐹 𝑑𝑥 2 𝐽=1 2𝐽 𝐽 4. Formulation of Beam Theories 𝑑2𝑓(𝑥) 2 = 2! 𝑄 𝑀 3(𝑥) = ∑𝐽=1 𝐾 𝐹 𝑑𝑥 3𝐽 𝐽 107 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 The kinematics of deformation of a beam can be 𝑑2𝑀− 𝑥𝑥 = 𝑞(𝑥) 𝑓𝑜𝑟 0 < 𝑥 < 𝐿 (21) represented by using various beam theories. Among them, 𝑑𝑥2 the EBT, TBT and RBT are commonly used [64-67]. Various By introducing the shear force 𝑄𝑥 and rewrite equation higher order beam theories are introduced in which the (21) in the following form straightness assumption is removed and the vanishing of 𝑑𝑀𝑥𝑥 𝑑𝑄𝑥 shear stress at the upper and lower surfaces is − + 𝑄𝑥 = 0, − = 𝑞(𝑥) (22) 𝑑𝑥 𝑑𝑥 accommodated. For this purpose, higher order polynomials incorporating either one, or more, extra terms [68-74] or By using Hooke’s law, one can obtain trigonometric functions [75,76] or exponential functions [77] 1 𝑧 𝑝 𝑑2𝑤0 are included in the expansion of the longitudinal point-wise 𝜎𝑥𝑥 = 𝐸(𝑧)𝜀𝑥𝑥 = − [(𝐸1 − 𝐸2) ( + ) + 𝐸2] 𝑧 2 (23) 2 ℎ 𝑑𝑥 displacement component through the thickness of the beam. If the equation (23) is put into equation (17), it is obtained, The higher order theories introduce additional unknowns that 𝑝 2 make the governing equations more complicated and provide +ℎ/2 1 𝑧 𝑑 𝑤𝑀𝑥𝑥 = − ∫ [(𝐸1 − 𝐸2) ( + ) + 𝐸 ] 𝑧 2 0 2 2 𝑑𝑧 = the solutions much costly in terms of CPU time. The theories −ℎ/2 2 ℎ 𝑑𝑥 𝑑2𝑤0 which are higher than the third order shear deformation beam −𝐷𝑥𝑥 2 (24) 𝑑𝑥 theory are seldom used because the accuracy gained by these theories which require much effort to solve the governing where equations is so little [66]. +ℎ/2 1 𝑧 𝑝 𝐷𝑥𝑥 = ∫ [(𝐸1 − 𝐸2) ( + ) + 𝐸2] 𝑧 2𝑑𝑧 (25) −ℎ/2 2 ℎ 4.1. Euler Bernoulli Beam Theory The substitution of equation (24) into equation (22) yields the EBT governing equation for a FGB subjected to the The following displacement field is given for the EBT, distributed load 𝑑𝑤 2 𝑢(𝑥, 𝑧) = −𝑧 𝑑 𝑑 2𝑤 (𝐷 0𝑑𝑥 2 𝑥𝑥 2 ) = 𝑞(𝑥) 𝑓𝑜𝑟 0 < 𝑥 < 𝐿 (26) 𝑑𝑥 𝑑𝑥 𝑤(𝑥, 𝑧) = 𝑤0(𝑥) (14) 4.2. Timoshenko Beam Theory where w0 is the transverse deflection of the point (x,0) which is on the mid-plane (z=0) of the beam. By using the The following displacement field is given for the TBT, assumption of the smallness of strains and rotations, the only 𝑢(𝑥, 𝑧) = 𝑧𝜙(𝑥) the axial strain which is nonzero is given by, 𝑑𝑢 𝑑2𝑤 𝜀 = = −𝑧 0𝑥𝑥 2 (15) 𝑑𝑥 𝑑𝑥 𝑤(𝑥, 𝑧) = 𝑤0(𝑥) (27) The virtual strain energy of the beam in terms of the where 𝜙(𝑥) is the rotation of the cross section. By using axial stress and the axial strain can be expressed by equation (27), the strain-displacement relations are given by 𝐿 𝑑𝑢 𝑑𝜙 𝛿𝑈 = ∫ ∫ 𝜎𝑥𝑥𝛿𝜀𝑥𝑥𝑑𝐴𝑑𝑥 (16) 𝜀𝑥𝑥 = = −𝑧 0 𝐴 𝑑𝑥 𝑑𝑥 where δ is the variation operator, A is the cross sectional 𝑑𝑢 𝑑𝑤 𝑑𝑤𝛾 = + = 𝜙 + 0𝑥𝑧 (28) area, L is the length of the beam, 𝜎𝑥𝑥 is the axial stress. The 𝑑𝑧 𝑑𝑥 𝑑𝑥 bending moment of the EBT is given by, The virtual strain energy of the beam including the virtual energy associated with the shearing strain can be 𝑀𝑥𝑥 = ∫ 𝑧𝜎𝑥𝑥𝑑𝐴 (17) 𝐴 written as, By using equation (15) and equation (17), equation (16) 𝐿𝛿𝑈 = ∫ ∫ (𝜎𝑥𝑥𝛿𝜀𝑥𝑥 + 𝜎𝑥𝑧𝛿𝛾𝑥𝑧)𝑑𝐴𝑑𝑥 (29) can be rewritten as, 0 𝐴 𝐿 𝑑2𝛿𝑤 where 𝜎𝑥𝑧 is the transverse shear stress and 𝛾𝑥𝑧 is the shear 𝛿𝑈 = − ∫ 𝑀𝑥𝑥𝑧 0 2 (18) 0 𝑑𝑥 strain. The bending moment and the shear force can be The virtual potential energy of the load q(x) which acts written respectively, at the central axis of the beam is given by 𝑀𝑥𝑥 = ∫ 𝑧𝜎𝑥𝑥𝑑𝐴, 𝑄𝑥 = ∫ 𝜎𝑥𝑧𝑑𝐴 (30) 𝐴 𝐴 𝐿 𝛿𝑉 = − ∫ 𝑞(𝑥)𝛿𝑤0𝑑𝑥 (19) 0 By using equation (28) and equation (30), one can If a body is in equilibrium, δW=δU+δV, the total virtual rewrite equation (29) as, work (δW) done equals zero. Then one can obtain, 𝐿 𝑑𝛿𝜙 𝑑𝛿𝑤 𝛿𝑈 = ∫ [ 𝑀𝑥𝑥 + 𝑄𝑥 (𝛿𝜙 + 0)] 𝑑𝑥 (31) 0 𝐿 𝑑2 𝑑𝑥 𝑑𝑥 𝛿𝑤 𝛿𝑊 = − ∫ ( 𝑀 𝑧 0𝑥𝑥 2 + 𝑞(𝑥)𝛿𝑤0) 𝑑𝑥 = 0 (20) 0 𝑑𝑥 The virtual potential energy of the load q(x) which acts After performing integration for the first term in at the central axis of the Timoshenko beam is given by equation (20) twice and since 𝛿𝑤 𝐿0 is arbitrary in (0 < x < L), 𝛿𝑉 = − ∫ 𝑞(𝑥)𝛿𝑤0𝑑𝑥 (32) one can obtain the following equilibrium equation, 0 108 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 Since the total virtual work done equals zero and the The usual bending moment and the shear force are, coefficients of 𝛿𝜙 and 𝛿𝑤0 in 0 6 The governing equations of the problem can be written 𝑑 = |𝑥 − 𝜉|/ℎ (57) in a similar way by replacing 𝑓(𝑥) given in equation (9) with 𝑤 (𝑥) and 𝜙(𝑥) and by using the SSPH basis functions as where 𝑑 is the radius of the CSD, ℎ is the smoothing length. 0 follows, G and 𝜆 are the parameters which are eliminated by the formulation of the SSPH method. ∑𝑀𝐽=1 𝜅𝑠𝐴 𝑀 𝑥𝑧𝐾2𝐽𝑊𝐽 + ∑𝐽=1[𝜅𝑠𝐴𝑥𝑧𝐾2𝐽 − 2𝐷𝑥𝑥𝐾3𝐽] Φ𝐽 = 0(51) The numerical solutions are performed according to the − ∑𝑀𝐽=1 2𝜅𝑠𝐴𝑥𝑧𝐾3𝐽𝑊𝐽 − ∑ 𝑀 𝐽=1 𝜅𝑠𝐴𝑥𝑧𝐾2𝐽 Φ𝐽 = 𝑞0 (52) following meshless parameters; the radius of the support domain (d) is chosen as 6 and the smoothing length (h) The SCF is assumed to be constant as 𝜅𝑠 = 5/6 for the equals to 1.1∆ where ∆ is the minimum distance between rectangular cross section, two adjacent nodes. The meshless parameters, d and h, are The boundary conditions regarding to the TBT are given selected to obtain the lowest error. as follows; Computed results obtained by using the SSPH method 𝑥 = 0, ∑𝑀 𝐾 Φ = 0 𝑎𝑛𝑑 ∑𝑀 𝐾 𝑊 = 0 𝑚 are compared with the analytical solutions, and their 𝐽=1 2𝐽 𝐽 𝐽=1 1𝐽 𝐽 accuracy and convergence properties are investigated by 𝑥 = 𝐿, ∑𝑀 𝑀𝐽=1 𝐾2𝐽 Φ𝐽 = 0 𝑎𝑛𝑑 ∑𝐽=1 𝐾1𝐽𝑊𝐽 = 0 𝑚 employing the global L2 error norm which is given by The analytical solution of this boundary value problem 𝑚 𝑗 𝑗 1/2[∑ 2𝑗=1(𝑣𝑛𝑢𝑚−𝑣𝑒𝑥𝑎𝑐𝑡) ] based on the TBT is given by 𝐿2 = 1/2 (58) 𝑗 [∑𝑚 2 4 3 4 2 2 𝑗=1 (𝑣𝑒𝑥𝑎𝑐𝑡) ] 𝑞 𝐿 𝑥 2𝑥 𝑥 𝑞 𝐿 𝑥 𝑥 𝑤 𝑇0 (𝑥) = 0 ( − 3 + 4) + 0 ( − 2) (53) 24𝐷𝑥𝑥 𝐿 𝐿 𝐿 2𝜅𝑠𝐴𝑥𝑧 𝐿 𝐿 The computed L2 error norms of the numerical solutions based on the EBT are given in Table 1. For the numerical 110 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 analysis different numbers of nodes are considered in the problem domain with 5 terms in TSEs expansion and varying gradation exponents. It is observed in Table 1 that the difference between the computed and analytical results is too small and the SSPH method almost gives the analytical solution of the problem. In Table 2, maximum deflection of the FGB is presented with varying aspect ratios and gradation exponent values. Table 1. L2 error norm for different number of nodes with varying gradation exponent (p) and aspect ratio L/h=10 - EBT Gradation Number of Nodes Exponent - 21 41 161 p -9 -8 -7 0 3.8621*10 9.0384*10 3.6786*10 -9 -8 -7 0.5 3.8606*10 9.0484*10 3.7665*10 -9 -8 -7 1 3.8636*10 9.0442*10 3.6774*10 -9 -8 -7 2 3.8591*10 9.0416*10 3.7251*10 -9 -8 -7 5 3.8635*10 9.0434*10 3.6998*10 Table 2. Maximum deflection (mm) of the beam with varying gradation exponent and different aspect ratios for 41 nodes - EBT Gradation Aspect Ratio (L/h) Exponent 5 10 20 50 (p) Fig. 3. Deflections of the beam computed based on the EBT 0 -0.0279 -0.2232 -1.7857 -27.9018 with varying number of nodes and the analytical solution. 0.5 -0.0195 -0.1561 -1.2489 -19.5145 Table 4. Maximum deflection (mm) of the beam with 1 -0.0176 -0.1414 -1.1312 -17.6753 varying gradation exponent and different aspect ratios for 41 2 -0.0164 -0.1317 -1.0539 -16.4681 nodes -TBT 5 -0.0152 -0.1221 -0.9776 -15.2758 Gradation Aspect Ratio (L/h) Exponent 5 10 20 50 Table 3. L2 error norm for different number of nodes with (p) varying gradation exponent (p) and aspect ration L/h=10 - 0 -0.0306 -0.2287 -1.7968 -27.9295 TBT 0.5 -0.0215 -0.1601 -1.2569 -19.5346 Gradation Number of Nodes 1 -0.0194 -0.1449 -1.1383 -17.6929 Exponent 2 -0.0180 -0.1349 -1.0603 -16.4839 21 41 161 (p) 5 -0.0166 -0.1250 -0.9833 -15.2900 0 4.1559*10-10 3.5002*10-9 5.9457*10-9 0.5 4.0629*10-10 3.5696*10-9 4.8358*10-9 -10 -9 -9 The global L2 error norms of the solutions based on the 1 3.8775*10 3.4994*10 5.6451*10 -10 -9 -9 TBT with different numbers of nodes in the problem domain, 2 4.1133*10 3.5803*10 2.8734*10 -10 -9 -9 5 terms in TSEs expansion and varying gradation exponents 5 3.9839*10 3.6220*10 4.3202*10 are given in Table 3. One can easily notice that the computed results are very close to analytical values when global L2 In Fig. 3, the numerical results in terms of transverse error norms are investigated. The results in Table 3 are deflections are compared with the analytical solutions with obtained for the meshless parameters d and h which gives the different number of nodes in the problem domain and best accuracy for each method. In Table 4, maximum varying gradation exponent values. The aspect ratio (L/h) is deflection of the FGB is presented with varying aspect ratios set as 50. It is observed in Fig. 4 that the SSPH method and gradation exponent values. As expected, the deflection agrees very well with the analytical solution. The transverse value increases either an increase or a decrease for the aspect deflection of the FGB computed by the SSPH method is ratio and the gradation exponent. It is clear that numerical virtually indistinguishable from that for the analytical solutions obtained by the SSPH method agree very well with solution. the analytical solution given in Fig. 5. 111 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 However, the convergence of the SSPH method increases when 7 terms in TSEs are employed. Table 7. Maximum deflection (mm) of the beam with varying gradation exponent and different aspect ratios for 161 nodes - RBT Gradation Aspect Ratio (L/h) Exponent 5 10 20 50 (p) 0 -0.0271 -0.2231 -1.7524 -27.2619 0.5 -0.0189 -0.1562 -1.2259 -19.0676 1 -0.0172 -0.1413 -1.1101 -17.2700 2 -0.0160 -0.1315 -1.0340 -16.0899 5 -0.0149 -0.1218 -0.9591 -14.9247 It is observed that the numerical solutions obtained by employing 7 terms in TSEs and using 161 equally spaced nodes in the problem domain agree very well with the analytical solution given in Fig. 5. Fig. 4. Deflections of the beam computed based on the TBT and the analytical solution. Table 5. L2 error norm for different number of nodes with varying gradation exponent (p) and aspect ratio L/h=10 – 5 terms in TSEs -RBT Gradation Number of Nodes Exponent 21 41 161 (p) 0 2.056779 2.056786 2.056786 0.5 2.167582 2.167589 2.167589 1 2.064060 2.064066 2.064067 2 1.924057 1.924063 1.924063 5 1.845563 1.845569 1.845569 Table 6. L2 error norm for different number of nodes with varying gradation exponent (p) and aspect ratio L/h=10 – 7 terms in TSEs - RBT Gradation Number of Nodes Exponent (p) 21 41 161 0 1.7794 1.6913 0.5618 0.5 1.8838 1.7994 0.4541 1 1.7866 1.6986 0.5545 2 1.6544 1.5619 0.6909 5 1.5820 1.4860 0.7665 Fig. 5. Deflections of the beam computed based on the RBT and the analytical solution By setting the aspect ratio as 10, the global L2 error 5.2. Cantilever Beam norms of the solutions based on the RBT are computed for different number of nodes, varying gradation exponent and For a cantilever FGB the static transverse deflections different number of terms in TSEs. By using 5 terms in under uniformly distributed load of intensity 𝑞0 is studied as TSEs, the accuracy of the SSPH method is not improved shown in Figure 6. when the number of nodes increases in the problem domain. 112 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 161 equally spaced nodes in the domain 𝑥 ∈ [0, 1]. The Revised Super Gauss Function given in equation (57) is used as the weight function. For the numerical solutions, the radius of the support domain (d) is chosen as 5 and the smoothing length (h) is chosen as 1.3∆. The meshless parameters, d and h, are selected to obtain the best accuracy. Computed results by the SSPH method are compared with the analytical solutions, and their rate of convergence and accuracy properties are investigated by using the global L2 error norm given in equation (58). In Table 8 the global L2 error norms of the solutions based on the EBT are given for different numbers of nodes in the Fig. 6. Simply supported FGB with uniformly distributed problem domain with varying gradation exponent and 5 load terms in TSEs expansion. The aspect ratio is set to 10. The As the physical parameters, the similar material computed deflection values of the FGB are almost equal to geometry and properties are used. The uniformly distributed analytical solution as seen Table 8 and Table 9. The load 𝑞0 is set to 10000 N/m. computed transverse deflection of the beam is virtually indistinguishable from that for the analytical solution as seen The governing equation of the problem is given in equation from Fig. 7. (49). The boundary conditions are given by; Table 8. L2 error norm for different number of nodes with 𝑥 = 0, ∑𝑀𝐽=1 𝐾2𝐽𝑊𝐽 = 0 𝑎𝑛𝑑 ∑ 𝑀 𝐽=1 𝐾1𝐽𝑊𝐽 = 0 𝑚 varying gradation exponent (p) and aspect ratio L/h=10 - 𝑥 = 𝐿, ∑𝑀𝐽=1 2𝐾3𝐽𝑊 𝑀 EBT 𝐽 = 0 𝑎𝑛𝑑 ∑𝐽=1 6𝐾4𝐽𝑊𝐽 = 0 The analytical solution of this boundary value problem based Gradation Number of Nodes on the EBT is given by Exponent 21 41 161 (p) 𝐸 𝑞 𝐿 4 𝑥2 𝑥3 𝑥4 -7 -6 -6 𝑤0 (𝑥) = 0 (6 2 − 4 3 + 4) (59) 0 9.3464*10 5.7715*10 7.7978*10 24𝐷𝑥𝑥 𝐿 𝐿 𝐿 -7 -6 -60.5 9.3463*10 5.7716*10 7.8008*10 The governing equations of the problem based on the TBT -7 -6 -61 9.3462*10 5.7715*10 7.7981*10 formulation are given in equation (51) and equation (52). The -7 -6 -62 9.3463*10 5.7716*10 7.7986*10 boundary conditions regarding to the TBT are given as -7 -6 -65 9.3462*10 5.7715*10 7.8015*10 follows; 𝑥 = 0, ∑𝑀 𝑀𝐽=1 𝐾1𝐽 Φ𝐽 = 0 𝑎𝑛𝑑 ∑𝐽=1 𝐾1𝐽𝑊𝐽 = 0 𝑚 Table 9. Maximum deflection of the beam for different 𝑀 𝑀 number of nodes with varying gradation exponent (p) and 𝑥 = 𝐿, ∑𝐽=1 𝐾2𝐽 Φ𝐽 = 0 𝑎𝑛𝑑 ∑𝐽=1 𝐾1𝐽 Φ𝐽 + aspect ratio L/h=10 – EBT ∑𝑀𝐽=1 𝐾2𝐽𝑊𝐽 = 0 Gradation Number of Nodes Analytical The analytical solution of this boundary value problem based Exponent Solution 21 41 161 on the TBT is given by (p) (mm) 4 0 -2.142857 -2.142857 -2.142856 -2.142857 𝑇 𝑞 𝐿 𝑥 2 𝑥3 𝑥4 𝑞 𝐿2 𝑥 𝑥2 𝑤0 (𝑥) = 0 (6 − 4 + ) + 0 (2 − ) (60) 0.5 -1.498715 -1.498715 -1.498715 -1.498715 24𝐷𝑥𝑥 𝐿 2 𝐿3 𝐿4 2𝜅 2𝑠𝐴𝑥𝑧 𝐿 𝐿 1 -1.357466 -1.357465 -1.357465 -1.357466 Based on the RBT, the governing equations of the problem 2 -1.264755 -1.264755 -1.264755 -1.264755 are given in equation (54) and equation (55). The boundary - - - -1.173184 conditions regarding to the RBT are given as follows; 5 1.1731843 1.1731842 1.1731842 𝑥 = 0, ∑𝑀𝐽=1 𝐾1𝐽 Φ𝐽 = 0 𝑎𝑛𝑑 ∑ 𝑀 𝐽=1 𝐾 1𝐽𝑊𝐽 = 0 𝑚 𝑀 𝑀 By using different numbers of nodes in the problem 𝑥 = 𝐿, ∑𝐽=1 ?̂?𝑥𝑥𝐾2𝐽 Φ𝐽 − ∑𝐽=1 2𝛼𝐹𝑥𝑥 𝐾3𝐽𝑊𝐽 = domain with 5 terms in TSEs expansion, the global L2 error 0, 𝑎𝑛𝑑 ∑𝑀 𝑀𝐽=1 𝐾1𝐽 Φ𝐽 + ∑𝐽=1 𝐾2𝐽𝑊𝐽 = 0 norms of the solutions obtained for the TBT are given in The analytical solution of this boundary value problem based Table 10. It is clear in Table 10 that the SSPH method on the TBT is given by provides satisfactory numerical results and rapid convergence to the analytical solution. In Table 11, 𝑤 𝑅(𝑥) = 𝑤 𝐸 𝑞 (𝑥) + ( 0 𝜇 ?̂? ) ( 𝑥𝑥 ) (2𝐿𝑥 − 𝑥2) + maximum deflection values computed by using different 0 0 2𝜆2 𝐴𝑥𝑧𝐷𝑥𝑥 number of nodes with varying gradation exponent are 𝑞 𝜇 ?̂? ( 04 ) ( 𝑥𝑥 ) [cosh 𝜆𝑥 + 𝜆𝐿 sinh 𝜆(𝐿 − 𝑥) − compared with the analytical solution. It is observed in Fig. 𝜆 cosh 𝜆𝐿 𝐴𝑥𝑧𝐷𝑥𝑥 𝑞0𝜇 ?̂?𝑥𝑥 1+𝜆𝐿 sinh 𝜆𝐿 8 that the SSPH method agrees very well with the analytical ( ) ( ) ( )] (61) 𝜆4 𝐴𝑥𝑧𝐷𝑥𝑥 cosh 𝜆𝐿 solution. The above boundary value problems are solved by using the SSPH method for different node distributions of 21, 41 and 113 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Armagan Karamanli, Vol.2, No.3, 2016 Fig. 7. Deflections of the beam computed based on the Fig. 8. Deflections of the beam computed based on the EBT and the analytical solution. TBT and the analytical solution. Table 10. L error norm for different number of nodes with Table 12. L2 error norm for different number of nodes with 2 varying gradation exponent (p) and aspect ratio L/h=10 - varying gradation exponent (p) and aspect ratio L/h=10 – 5 TBT terms in TSEs - RBT Gradation Number of Nodes Gradation Number of Nodes Exponent Exponent 21 41 161 21 41 161 (p) (p) 0 1.7557 1.7732 1.7868 -8 -7 -8 0 1.1737*10 3.2575*10 6.0033*10 0.5 1.8593 1.8778 1.8921 -8 -7 -8 0.5 1.0989*10 3.1489*10 5.3044*10 1 1.7615 1.7791 1.7927 -8 -7 -8 1 1.1602*10 3.2470*10 6.6439*10 2 1.6317 1.6481 1.6607 -8 -7 -8 2 1.1786*10 3.4013*10 5.8399*10 5 1.5523 1.5729 1.5850 -8 -7 -8 5 1.2413*10 3.4943*10 6.5123*10 Table 13. L2 error norm for different number of nodes with Table 11. Maximum deflection of the beam for different varying gradation exponent (p) and aspect ratio L/h=10 – 7 number of nodes with varying gradation exponent (p) and terms in TSEs aspect ratio L/h=10 - TBT Gradation Number of Nodes Gradation Number of Nodes Analytical Exponent 21 41 161 Exponent Solution (p) 21 41 161 (p) (mm) 0 1.7309 1.8455 1.5222 0 -2.165079 -2.165079 -2.165079 -2.165079 0.5 1.8357 1.9472 1.6351 0.5 -1.514786 -1.514786 -1.514786 -1.514786 1 1.7368 1.8512 1.5287 1 -1.371583 -1.371583 -1.371583 -1.371583 2 1.6054 1.7244 1.3857 2 -1.277342 -1.277342 -1.277342 -1.277342 5 1.5299 1.6518 1.3035 5 -1.184540 -1.184540 -1.184540 -1.184540 The global L2 error norms of the solutions based on the RBT are given in Table 12 where different numbers of nodes and gradation exponents are considered with 5 terms in TSEs expansion. 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[63] Fatahi, H., Nadjafi, JS, Shivanian, E, New spectral meshless radial point interpolation (SMRPI) method for the two- 117 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 Fluorescent Lamp Modelling and Electronic Ballast Design by the Support of Root Placement Ibrahim Aliskan*‡, Ridvan Keskin* * Department of Electrical and Electronics Engineering, Faculty of Engineering, Bulent Ecevit University, 67100 Zonguldak, Turkey (ialiskan@beun.edu.tr, ridvan.keskin@beun.edu.tr) ‡ Corresponding Author: Ibrahim Aliskan, Department of Electrical and Electronics Engineering, Faculty of Engineering, Bulent Ecevit University, 67100 Zonguldak, Turkey, Tel: +090 3712911570, Fax: +90 3722574023, ialiskan@beun.edu.tr Received: 28.07.2016 Accepted: 02.09.2016 Abstract-It is presented that high frequency electronic ballast for fluorescent lamps is designed with root placement method using natural frequency and damping ratio. Also, a fluorescent lamp is designed as to have dynamic resistant. The method proposes simple mathematical calculations instead of complex mathematical calculations and the approaches based one of the component of resonant tank, which arbitrary chosen value. Also it is capable to provide accurate values, which can be employed in new types to ballasts. Natural frequency and damping ratio, which are parameters of the method, are chosen switching frequency, 0.707, respectively. Transfer function of electronic ballast circuit is calculated by means of proposed method. After that, components of the circuit are find out. 220 V(rms) voltage was achieved at ignition and obtained 30 W lamp power in state space operation. Electronic ballast design and a fluorescent lamp are made of using Matlab/Simulink interface and the results are presented. Keywords Electronic ballast, design parameters, switching frequency, fluorescent lamp. 1. Introduction lamps to be created after thermal radiation. When you turn on the electricity, it goes through the one electrode to another in Humankind is always in the search of new energy the fluorescent lamp. When the initial voltage reached, sources and efficient use of current sources in view of the mercury is vaporized and ultraviolet lights are emitted. By limited energy sources in earth. The economic crisis in the the help of phosphorus placed in tube, this ultraviolet light world in last years has shown that energy saving concerns has transforms to the emitted light to be seen by our eyes [3]. to consider to preserve natural resources. Many new Fluorescent lamps have many advantages in comparison developments have been applied to the traditional electrical with regular bulbs. They are more expensive but have more equipment to improve the efficiency. Efficient usage of than 10 times long life than regular bulbs. Because light is electricity, as a transformation phase of different energy emitted from a larger source (not a single point like light types, has more importance. One of the most widely used bulbs) in florescent lamps, it emits more light. Blue light fields of electricity is lighting. The most widely used light emitted by florescent bulbs are better for the eye comfort. An sources are incandescent and fluorescent lamps in lighting 18 W fluorescent lamp can emit light as much as a 75 W [1]. Even light bulbs are considered as the prior source of regular light bulb. It means that fluorescent lamps consume lighting, in 20th century, fluorescent lamps are developed to less energy and emit more light, which ends up in around efficiently use energy. Usage of florescent bulbs in schools, 75% energy efficiency. In addition that, as the ballasts used offices and other places made the development of more in florescent lamps are developed, it is expected to increase efficient fluorescent lamps a necessity [2]. their efficiency [4], [5], [6]. Fluorescent lamps or fluorescent tubes use electricity for The ballast works as a part of a florescent lamp to reach heating mercury and vaporing through filaments to produce starting voltage and to limits the current in the lamp terminals light. Light is produced after many phases in fluorescent upon reached steady state. As the gas discharge starts, at 118 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 ignition, current continuously increases and lamp voltage frequency and damping ratio, which is parameters of the decreases. If resistance of the lamp is formulized as method, is chosen as natural frequency is switching frequency Rlamp=dV/dI, it is seen that the resistant has a negative slope and damping ratio is 0,707 with the purpose of optimum or the lamp has negative resistance character (NTC). This efficiency [18]. Also it is focused on the design of an requires the current to be limited. In less powered lamps, to optimum resonant tank by considering the lamp equivalent limit the current, serial resistances may be used. However, resistant Rlamp is variable at high frequency. Using this this causes to loss power. Therefore, using ballast is a better method increases the gain and efficiency of the circuit by way to save energy. There are two main type ballasts as means of calculate components of circuit exactly. electromagnetic ballasts and electronic ballasts [3]. The paper divided into five sections. In section 2, the Inductive ballasts, which named as magnetic or fluorescent lamp resistance is designed as dynamic electromagnetic, are made of core rounded with aluminium resistance model. Instead of voltage and current parameters, or copper. In a fluorescent lamp, network voltage of 220V power of the fluorescent lamp is considered as a parameter is not enough to start lighting in the beginning. It requires in this approach. In section 3, design of the electronic ballast around 300V for starting firing. Therefore, an auxiliary is presented. In section 4, the simulation study is presented. device is necessary to generate high breakdown voltage for In section 5, the results are shared. start-up and to stabilize lamp current. This device is the “starter” as a switch and used in the lamps to start lighting 2. Fluorescent Lamp Model With Dynamic Resistant in the beginning. It does not work during the regular working or steady state times of fluorescent lamps. Circuit topology of a basic high frequency electronic Electronic ballasts require higher frequency than ballast system is shown in Fig. 1. While it is supplied by dc magnetic ballasts (fe > 20 kHz). They do not require a starter power supply, there is no need for power factor corrector to initiate start-up voltage. In other words, they can give the (PFC) circuits and the circuits to prevent total harmonic start-up voltage themselves. Electronic ballasts are 10-20% distortion (THD). The parallel resonant inverter behaves like more efficient than the inductive ballasts [7]. When more a current source, which can be used to stabilize fluorescent lamps are used in a system, this efficiency becomes more lamp current [19]. important. The more efficient on lighting systems the less heat is emitted. It is listed below that advantages of electronic ballasts in compared with inductive ballast: K1  Increases the effectiveness of the lamp and all lighting T1 Is system.  Prevents light vibration and stereoscopic events. + Ls Cs +  Increases power factor and does not need compensation. Vdc T2 Vs Lamp Vo Cp  Enables to use light current in any degree. K2  With lower heat increase, heat loss is decreased too. - - DC/AC  Does not have noises. RESONANCE TANK TRANSFORMATION  Two lamps can work through a ballast. Fig. 1. Basic circuit configuration of an electronic ballast with half bridge series-resonant parallel-loaded inverter  Small size, less weight, high frequency [8] - [13]. While the circuit is suppling by dc battery, sinusoidal In recent years, there has been quite works and signal is obtained at desired high frequency level by use of researchers are studying about this topic. These works are T1 and T2 Mosfets, active power switches. This active power about design to boosts efficiency and gain of electronic switches supplied with K1 and K2, square waves generators, ballasts. As so the works based on lamp arc, it exists that are turned on and off alternately with a short dead time to based on one of the components of the circuit as well. These drive the load resonant circuit at a high frequency. The high-frequency fluorescent lamp models are used for parallel branch of resonant tank consists of a parallel optimization studies [3], [4], [5], [14], [15], [16], [17]. capacitor, Cp, and a fluorescent lamp. Lamp Series branch of However, they are not enough finding components of the the circuit is formed by an inductor, Ls, and a capacitor, Cs. circuit and procuring optimum efficiency on account of the Cp is to provide a sufficiently high voltage across the lamp fact that it is not to calculate properly the components. In terminals during starting transient, afterwards a proper ac addition, Methods of them are based on one of the current at the steady state [20]. component of the resonant tank, which arbitrary chosen value, or to have complex resolutions. When lamp is off state, it behaves like an open circuit, resistant of lamp is almost equal to infinite value due to In this study, circuit parameters and components of mercury mixture which is in fluorescent lamp tubes. electronic ballast are calculated by using this method. The However, the mixture is ionized and the resistant value design is made with Matlab/Simulink interface. Natural decrease swiftly when the lamp is on state. Therefore, the 119 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 studies calculated resistant of lamp as a constant or with Transfer function of the circuit indicated in Fig.1 is find R=V/I equation is not given proper calculation [4]. by following steps which is below and its poles are named as s1, s2, s3. After that, parameters of the circuit are calculated Various dynamic resistant approaches are developed to in consequence of committed calculations using natural calculate resistant of fluorescent lamps [4]. The approaches frequency and damping ratio. As for gain of circuit, based on voltage and current of the lamps are not given numerator of (3) must be maximize. Electronic ballast expected results due to the lamp resistant behaves as (NTC). parameters are presented in table-1 in accordance with this That’s why in this paper an approach based on lamp power to foresight. calculate resistant of the lamp is focused. A monotonic double exponential model is chosen to represent the electric G(s) V 0 /Vs (2) characteristics of the lamp at high frequency optimally. iwLs  XLs (3) R  a.e(b.Plamp)  c.e(d .Plamp)lamp (1) 1/(iwCs)  XCs (4) This equation is derived from a curve fitting to the experimental data of equivalent resistance versus average 1/(iwCp)  XCp (5) power [21]. A curve of equivalent resistance versus average power is presented in Fig.2 as a consequence of simulation XCp.Rlamp made in Matlab/Simulink. V 0  i(s).( ) (6) (Xcp  Rlamp) XCp.Rlamp Vs  i(s).(XLs  XCs  ). (7) ( XcpRlamp) Equation (6) is divided by equation (7) or from voltage- divide law, 1 Rlamp  V 0  iwCs (8) Vs iwLs 1/(iwCs)  (Rlamp 1/(iwCp)) then transfer function of the circuit is found out as a third order function in s-domain. Fig. 2. Curve of Lamp resistant versus Average power in Simulink s Cp.LsG(s)  (9) 2 3. Electronic Ballast Design 3 s (Cp Cs).s 1s    Cp.Rlamp Cp.Cs.Ls Cp.Cs.Ls.Rlamp The purpose is to find values of the circuit parameters with mathematical calculation instead of based on one of The circuit is stable because all of poles are located left circuit parameters or set value. By using this method, we find side of s-domain. As to the zero of transfer function, locates the parameter optimally. The control parameter used to vary at origin owing to structure of circuit. These circumstances the output power in all single stage topologies is switching can be seen from the transfer function. However, the gain frequency. These are variable frequency methods that higher was interfered by way of coefficient of the zero. frequency results in lower power delivered to the lamp [14]. Open representation of fluorescent lamps is shown in First, damping ratio and switching frequency is chosen 0.707, Fig.3. Rf resistance represents filaments of lamps situated at 56.82 kHz, respectively. Then transfer function of circuit is terminals of the lamps. The resistance value is chosen using find out. Poles and zeros of the function is calculated. System experimental data [15]. identification is evaluated by using transfer function of the circuit. Rf Rf Table 1. Parameters of the circuits ζ Damping ratio 0.707 Rlamp wn Natural frequency 358.14 k rad/s 5 s1 A root of the transfer function (-2.53+2.53i).10 s2 5A root of the transfer function (-2.53-2.53i).10 5 Rf Rf s3 A root of the transfer function -3.58.10 A Fluorescent Lamp Ls Series inductor 1.31 mH Cs Series capacitor 14.4 nF Fig. 3. Representation of a fluorescent lamp with filament Cp Parallel capacitor 2.97 nF resistances 120 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 4. Simulation Implementation of Fluorescent Lamp Model Table 2. Monotonic double exponential function parameters and other values The goal is to make simulation study ideally to comprehend behaviour of fluorescent lamp system shown in Parameter Explanation Value Fig.1. Matlab/Simulink interface is used as computer a Value of variable 8147 environment to implement the complex circuit easily. b Value of variable -0.2113 Applied circuit is presented in Fig.4. It is supplied with c Value of variable 1433 battery to have 220-240 V. The mosfets are triggered with d Value of variable -0.5353 0.5 fill rate by using a logical gate and a pulse generator. Rf Resistanceof filaments 6Ω x4 Also, they supply the resonance tank. Dynamic resistant Vdc DC Voltage 236 V model of the fluorescent lamp which is subsystem of Fig.4 is fs Switching frequency 56.82 kHz presented in Fig.5 clearly. Equation 1 is simulated using a |Iin| Amplitude of the current (Iin) 0.26 A function block parameter. A Controlled current source is used |Vin| Amplitude of input voltage 236 V to execute dynamic resistant model. Rf represents a filament (Vin) resistance of the fluorescent lamp shown in Table 2. In Rlamp Equivalent resistance of the 389 Ω addition, other data used in Fig.4 and parameters of the lamp monotonic double exponential function is shown in Table 2 Plamp Power of the lamp 26.1 W as well. Fig. 4. A high frequency electronic ballast circuit with a dynamic resistant fluorescent lamp model Fig. 5. Demonstration of dynamic resistant and the fluorescent lamp model 121 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 5. Results High frequency electronic ballast with dynamic resistance fluorescent lamp model, presented in Fig.4, whose subsystem is shown in Fig.5, is run. The results are presented in following figures. To design the circuit Matlab/Simulink is used. Lamp voltage and current are presented with general overview in Fig.6, with root mean square forms. It is seen clearly that Lamp voltage is high at transient response because of the reason mentioned in section 1. This means that, the lamp can be run and the resistance model is successful. In addition, before ignition, the lamp pretends Fig. 8. Voltage-current of the lamp versus time at steady open circuit because its resistant equals to roughly infinite state operation value. Then in the ignition the current increases sharply due to decreasing of the resistant. This can be comprehended by Figure 9 is represented to behave of the lamp at ignition. means of reviewing to Eq .1. Finally, the current is suitable Especially the voltage signal has become sinusoidal signals value in steady state operation. varying its amplitude due to variable lamp resistant in 0.12 sec implemented the ignition. Sinusoidal the current and the voltage signals are obtained 0.12 sec after lamp operating as to have constant amplitude in steady state. The high voltage at ignition able to be seen in that figure as well. This voltage is sufficient to ignite the lamp. The Voltage, Vs, with square form, and Current, Is, with sinusoidal form, waveforms are presented in Fig.10. To expect from the resonant circuit is to minimize the phase difference between voltage and current of series branch. This expectancy is satisfied thanks to the given ballast circuit, designed in frequency domain. Fig. 6. Lamp Voltage and current versus time (a) Lamp current vs time (b) Lamp voltage vs time Figure 7 is presented to better understand the relationship of lamp voltage and current at ignition. On the other hand, there is a lamp dynamic resistance variation (rlamp  Vlamp /I . lamp ) Voltage and current waveforms of the lamp in lamp running is presented in Fig.8, with sinusoidal waveforms. It can be seen that phase difference between them nearly equal to zero. Thus ensuring that the lamp represents a pure resistive load with high linearity at high operating frequency. Fig. 9. The signals of the lamp versus time at ignition Also they have no fluctuations. (a) Current of lamp vs time (b) Voltage of lamp vs time Fig. 10. Input Current and voltage waveforms after just Fig. 7. Lamp voltage versus lamp current switching process 122 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Ibrahim Aliskan et al., Vol.2, No.3, 2016 6. Conclusion Push-Pull Electronic Ballasts”, Applied Power Electronics Conference and Exposition, IEEE, vol. 1, pp. 421-426, This paper presented that root placement method about February 1994. to calculate the electronic ballast parameters through roots of the transfer function. Resonance tank circuit has been [9] Istok R., “High Frequency Emissions of Electromagnetic and Electronic Fluorescent Lamps” , IEEE International Symposium developed to base on operating point resistant of the on Applied Computational Intelligence and Informatics , fluorescent lamp through roots of frequency domain. Romania, pp. 21-23 , 21-23 May 2015. Modelling of a dynamic resistance in software environment depends on the view of researchers. It can be seen that [10] Sheeraz A.; Faizan A.; S. Riaz-ul-Hasnain; Duri S.; Sagib J. success of this in Fig.5. The method has simple mathematic “Electronic Ballast Circuit Configurations for Fluorescent Lamps” Power Generation System and Renewable Energy calculations and is capable to provide accurate values, which Technologies (PGSRET), IEEE Conference Publications, pp. can be employed in new types to ballasts. Whereas, previous 1–8, 2015. studies about this topic were based on one of the circuit parameters or a function which is complex. This study is [11] A. Vitanza, R. Scollo, A. Hayes “Electronic Fluorescent Lamp different to them from this aspect. In other words, this is Ballast”, Application Note, Microelectronics,1999. innovator side of the method. [12] Y. Ji, R. Davis, “Starting Performance of High-Frequency Electronic Ballast for Four-Foot Fluorescent Lamps” IEEE A critical issue that has been validated in this study is the Transactions on Industry Applications, vol. 33, pp. 234-238, starting voltage needed by fluorescent lamps is supplied. This January/February 1997. can be seen from Fig. 6, 9. The phase difference between lamp voltage and current could be seen in Fig.8. It is nearly [13] R. A. Gupta, R. Agarwal, H. Soni, M. Ajay, “Design and Simulation of Single Stage High PF Electronic Ballast with zero value. Simulation studies are made to observe success in Boost Topology for Multiple Fluorescent Lamp” vol. 2, pp. virtual environment putting in process of integrated structure. 323-331, November 2009. To perform simulations of the integrated structure, comprising a component to have a dynamic resistance, and [14] A. A. Mansour, O. A. Arafa, “Comparative study of 250 W reaching the instantaneous value of the electrical signal is one high pressure sodium lamp operating from both conventional and electronic ballast”, Journal of Electrical Systems and of the success of this paper. The mathematical value of Information Technology, vol.1, pp: 234-254, December 2014. equation (1) and the dynamic resistance value obtained on the simulation environment is equal. This is another success of [15] Wakabayashi F. T., Dantas F. D., Pinto J. O. P., Canesin C. A. the simulation. “Fluorescent Lamp Model based on Equivalent Resistances, Considering the Effects of Dimming Operation” 2005 IEEE 36th Power Electronics Specialists Conference, pp. 1136-1141, References 2005. [1] U.S. Lighting Market Characterization, Building Technologies [16] Ribarich T. J., Ribarich J. 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[19] Shao J., Stamm T., “Cost Effective High Performance LED [4] R. Verderber, “Electronic Ballast Improves Efficiency” Elec. Driver Powered by Electronic Ballasts”, IEEE Applied Power Consultant, vol. 60, pp. 22-26, November 1980. Electronics Conference and Exposition (APEC), Long Beacg, [5] J. R. Coaton, A. M. Marsden, Lamps and Lighting 4th Edition, CA, pp. 3659-3662, 20-24 March 2016. 4 th ed. Routledge; November 1, 1996. [20] Moo C. S., Cheng H. L., Lin T. F., Yen H. C. “Designing a [6] J. Choi, “LED Driver Compatible with Electronic Ballast”, Ph. Dimmable Electronic Ballast with Voltage Control for D. Dissertation, Dept. Elect. Eng. KAIST, 2013. Fluorescent Lamp” Industrial Electronics, 1999. ISIE '99. Proceedings of the IEEE International, Bled, pp. 786 - 791, 12- [7] Cheng C. A., Liang T. J., Chuang C. M., Chen J. F. “A Novel 16 July 1999. Method of Using Second-Order Lamp Model to Design Dimmable Fluorescent Lamps Electronic Ballast” Industrial [21] Perdigão M., Saraiva E. S., “Electronic Ballast with Wide Electronics Society, The 27th Annual Conference of the IEEE, Dimming Range: Matlab-Simulink Implementation of a Double pp. 1033-1037, 29-02 November/December 2001. Exponential Fluorescent Lamp Model” Spanish Portuguese Congress on Electrical Engineering, Spain, pp. 1-6, 02-30 June [8] Yu T. H., Wu L. M., Wu T. F., “Comparisons among Self- 2005. Excited Parallel Resonant, Series Resonant and Current-Fed 123 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 Dynamic Spectrum Access: A New Paradigm of Converting Radio Spectrum Wastage to Wealth ‡ Jide J. Popoola , Oluwaseun A. Ogunlana, Ferdinad O. Ajie, Olaleye Olakunle, Olufemi A. Akiogbe, Saint M. Ani-Initi, Sunday K. Omotola Department of Electrical and Electronics Engineering, Federal University of Technology, P.M.B. 704, Akure, Ondo State, Nigeria (jidejulius2001@gmail.com, ayolana2002@yahoo.com, odeyfeddy@yahoo.com, kunvicleye2011@yahoo.com, ayodejiakiogbe@gmail.com, saintzoba@gmail.com, omotolasunday@yahoo.com) ‡ Corresponding Author: Jide J. Popoola, Department of Electrical and Electronics Engineering, Federal University of Technology, Akure, Ondo State, Nigeria. Tel: +23 4803413/1860, jidejulius2001@gmail.com Received: 16.08.2016 Accepted: 31.08.2016 Abstract-The study presented in this paper reveals the limitations of the current fixed radio spectrum allocation policy as a major bottleneck for availability of radio spectrum for emerging wireless services, devices and applications as a result of its contributions to current radio spectrum artificial scarcity and underutilization problems. In investigating these problems scientifically, series of radio spectrum occupancy studies were carried out in developed nations of the world with little or none in most under-developed nation like Nigeria. In order to ascertain the usage profile of radio spectrum in under-developed nation like Nigeria, actual radio spectrum usage in three different locations in South-West Geo-political zone of Nigeria was carried out. The study was conducted using Aaronia AG HF-6065 V4 spectrum analyzer. The results obtained like other similar studies conducted in other parts of the world show that the usage of radio spectrum varies with time, space and frequency. The results also show that the actual radio spectrum usages in the three locations for the frequency range of 80-2200 MHz vary from 0.08% to 64.4%. In addition, the paper enumerates various ways of converting the current wasting spectrum holes to wealth as well as some economic advantages of dynamic spectrum access as a flexible radio access policy that can replace the current fixed radio spectrum allocation policy without compromising the performance of the existing radio being governed by the fixed spectrum allocation policy. Keywords Spectrum holes, spectrum occupancy measurements, dynamic spectrum access, cognitive radio, spectrum trading. 1. Introduction wireless services, devices and applications unless some of the existing licenses are discontinued [1]. In addition, Over the past two decades, the exponential growth in according to Buddhikot and Ryan [2], current spectrum demand for radio or wireless communication services, management also has another serious operational problem as devices and applications has brought with it the need for a several licensed bands are not efficiently utilized with change in the way radio spectrum is being regulated. utilization varying dramatically over frequency, space and Currently, the radio spectrum regulatory bodies worldwide time. Furthermore, it was discovered through actual spectral are of the opinion that the rigid spectrum management policy occupancy measurements that vast portions of the licensed granting exclusive right to use licensed spectrum is still radio spectrum are randomly or rarely used by the licensed efficient. However, observations have shown that the idea of users [3-10]. For instance, a study conducted by the Federal statically apportioning of radio spectrum into blocks and Communications Commission (FCC) reported by Popoola allocated for specific purposes as well as licensed to specific and Van Olst [11], showed that usage of the licensed radio user or operator on either short or long term is long overdue spectrum varied from 15% to 85% in the United State of and inefficient. This is because majority of the available America (USA). radio spectral resources have already been licensed to users indicating that there is little or no room to add any new 124 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 Also, as reported by [11], similar actual spectral bands considered. The result of the study, gave an average occupancy measurements showed that as little as 22% of occupancy rates of 8.8% and 52.4% respectively for both the allocated spectrum is utilized in urban areas and less than 3% uplink and downlink in GSM900 band. The corresponding is being utilized in rural areas buttressing the fact that usage results for the uplink and downlink occupancy rates for of radio spectrum varies with space. Similarly, as reported by GSM1800 band obtained in [16] are 0.6% and 13.6% [11], observation from actual radio spectrum occupancy respectively. Also, the obtained uplink and downlink measurements conducted in downtown Berkeley showed that occupancy results in the study are 0.56% and 48.7% allocated frequency bands to licensed users are underutilized respectively for the UMTS2100 band while the especially in the 3-6 MHz, while some other frequency bands corresponding results for the LTE2600 band are 0% and are rarely occupied and the remaining frequency bands are 0.6% respectively. heavily occupied showing that radio spectrum usage also Similarly, in Nigeria, one of the studies on spectrum vary with frequency. A typical result of these measurements occupancy measurements in searched literature was presented in [9] is shown in Fig.1. From these observations, conducted and published by [14]. The study presented in [14] according to [11], the concept of spectrum holes was was conducted at Gwarinpa District in Abuja. The results introduced, which was defined in [10, 12] as bands of obtained by [14] showed that the variation of usage of frequencies assigned to primary users (PUs) also known as licensed spectrum in Abuja, the Nigeria Federal Capital licensed users but at a particular time and in specific Territory, ranges from 17% to 26% at 700 – 2400 MHz geographical location the bands are not being utilized by the frequency bands considered. Furthermore, the results of licensed users. another recent study on spectrum occupancy measurements [17], which were conducted in Abuja and Katsina both in Nigeria show variations in spectrum usage in the two locations with occupancies variations from 0.45% to 26%. Thus, in order to ascertain the level of licensed spectrum usage in other parts of the country, the study reported in this paper was embarked upon. It was embarked upon to ascertain whether or not dynamic spectrum access also known as opportunistic spectrum access (OSA) can be proposed in Nigeria as in other nations of the world. The study was conducted in three state capitals (Ado-Ekiti, Akure and Ikeja) in the South-West Geopolitical zone of Nigeria. The full details on how the occupancy measurements were conducted are presented in Section 3 of this paper. The rest of the paper is organized as follows: In Section 2, a brief background on dynamic spectrum access (DSA) and cognitive radio technology as an enabler of DSA is presented. The details on the field measurements conducted to evaluate the spectrum occupancy in the study areas are Fig. 1. Typical spectrum under-utilization profile [9] presented in Section 3. The results obtained in Section 3 Generally, according to Najashi and Feng [13], spectrum were analyzed and discussed in Section 4. The economic occupancy measurements have been used to ascertain the advantages of DSA in converting spectrum holes to wealth level of spectrum utilization by licensed users. The essence by the regulatory bodies and/or licensed users are also of spectrum occupancy measurements is to prove the need presented in this section. Section 5, which is the last for deployment of another radio spectrum access technology section, concludes the paper. for both effective and efficient radio spectrum management. However, out of the several spectrum occupancy 2. Brief on DSA and Cognitive Radio Technology measurements conducted all over the world, it was discovered that most were done in USA and Europe with few Dynamic spectrum access also known as OSA is defined in Asia and Africa [14]. For instance in South Africa, the as a new spectrum sharing paradigm that allows unlicensed spectrum occupancy measurements carried out in the or secondary user (SU) to access the idle or unused spectrum Hatfield area of Pretoria for ultra-high frequency (UHF) otherwise called spectrum holes or white spaces in the band, global system for mobile communications (GSM) 900 licensed spectrum band. It is a flexible radio spectrum access MHz and GSM 1800 MHz bands by [15] show variations in policy to alleviate the current problems of spectrum scarcity usage of the three bands. The UHF band for instance has an and spectrum underutilization in order to increase spectrum approximately occupancy of 20% while those of GSM 900 utilization [18]. The concept of DSA is to find a means of MHz and GSM 1800 MHz bands are at approximately 92% accessing the unused portion of already assigned licensed and 40% respectively. Similar study carried out in Kampala, spectrum without interfering with the transmission of the PU Uganda capital recently using GSM900, GSM1800, the as illustrated in Fig.2. The type of radio that enables SU to universal mobile telecommunications system 2100 operate in idle portion of the licensed spectrum in this (UMTS2100) and long term evolution 2600 (LTE2600) opportunistic manner is known as cognitive radio. bands presented in [16] shows variations in those frequency 125 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 The process of monitoring the available spectrum band in order to detect the presence of unused spectrum is known as spectrum sensing. Spectrum analysis on the other hand is a means of estimating the characteristics of the detected spectrum holes while spectrum decision is a means of determining the data rates and the transmission mode as well as the bandwidth of transmission with a view to choosing appropriate spectrum band according to spectrum characteristics and user requirements. As availability of spectrum hole is essential for adoption of DSA, the method employed to ascertain the availability of spectrum holes and the level of radio spectrum usage in this study are presented in the next section. 3. Methodology In carrying out the study presented in this paper to ascertain the availability of spectrum holes in Nigeria for proposing adoption of DSA in the country, actual spectrum occupancy measurements were carried out in three states out Fig. 2. Spectrum hole concept [9] of the six states that made up of the South-West Geo- Political zone in Nigeria. The actual spectrum occupancy Cognitive radio (CR) technology is the main technology measurements were conducted in Ado-Ekiti, Akure and that enables already assigned spectrum to be used in a Ikeja, which are respectively the state capitals for Ekiti, dynamic manner. It is defined as a radio that can change its Ondo and Lagos states respectively. The three locations were transmitter parameters based on interaction with the were chosen as the good representation of the geo-political environment in which it operates [9]. The cognitive zone due to their socio-economic developments, industrial capability of CR enables its real time interaction with its activities, and population size. environment to determine appropriate communications parameters and adapt to the dynamic radio environment. In Lagos state, the actual spectrum occupancy According to [9], the tasks required for CR to perform this measurement was conducted in Ikeja, longitude 0 / // 0 / // adaptive operation and ensuring interference free 3 20 28 E and latitude 6 38 13 N . This study communication with the PU of the spectrum is referred to as location is a densely populated residential and business area the cognitive cycle. The three main steps in cognitive cycle of the state, which is predominantly characterized by schools, as shown in Fig.3 are spectrum sensing, spectrum analysis banks, office blocks, shopping complex and residential and spectrum decision. buildings. The location is strategic and ideal for the study because of its proximity to radio and television broadcasting stations, mobile phone base stations, military headquarter, harbour and airport among others radio spectrum users in Radio that vicinity. Likewise, in Akure, the study location lies at 0 / // 0 / // Environment longitude 5 11 42 E and latitude 7 15 0 N while RF Stimuli the study location in Ado-Ekiti lies at longitude Transmitted 50 13/ 47// 0 / //Stimuli E and latitude 7 35 16 N . These study Signal locations are equally strategic locations with proximity to Spectrum Signal Primary User different radio spectrum licensed users. In the three locations, Mobility Detection the same measurement setup was employed, which consists Spectrum Spectrum of an Aaronia AG HF-6065 V4 spectrum analyzer with a Mobility Sharing Detection Sensing range of 10 MHz - 6 GHz, an Aaronia AG HyperLOG antenna, a laptop system that is connected to the spectrum Sensing Sharing Decision analyzer via a USB cable, and an MCS software specially Request Spectrum designed to run on Aaronia AG spectrum analyzers as shown Channe Hole in Fig.4. l Request Capacit Hole Spectrum y Spectrum Characterization Decision Capacit Characterization y Decision Fig. 3. Cognitive cycle [19] 126 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 channel. On the other hand, if the threshold metric is low it will lead to over estimation of the channel under consideration. Thus in determining the decision threshold values for each band at each location for this study, the average noise level was first determined by connecting a 50  resistor to the spectrum analyzer [16]. The decision threshold was set by adding 3 dB to measured thermal noise. The decision threshold obtained varies from one location to another as well as the frequency band since the noise level varies with locations and frequencies. The decision threshold values employed are presented in Table 1. The threshold values were used in determining the actual spectrum occupancy for each frequency band by finding the ratio between the points above the threshold to the total number of points during the Fig. 4. Measurement set-up measurement period. The actual spectrum occupancy (SO) is defined using the relation; The block diagram representation of the measurement set-up is shown in Fig.5. The arrows in Fig.5 show the NSO  0 (1) direction of flow of signal in the set-up. The antenna receives N the signal, the meter quantifies it, and the values of the quantified signals are stored in the laptop which also serves where N0 is the total number of points above the threshold as the display unit for the set-up. value and N is the total number of points during the measurement period. The results obtained from the measurements conducted are presented and discussed in the next section. Antenna Meter Laptop 4. Results and Discussions Four actual spectral usage profiles for the three locations Fig. 5. Block representation of the measurement set-up for 80 – 150 MHz, 400 – 960 MHz, 900 – 1300 MHz and 1900 – 2200 MHz bands out of the eight frequency bands In determining the availability of the spectrum hole in considered are presented graphically in Figs.6-9. The Figures any channel, energy detection method was employed, which show variations in the spectral usage in those frequency necessitate the determination of threshold value for each bands in the three locations. Also, the results of the actual frequency band considered in the three locations. This is spectral usage in the three locations show variations in the because when energy detection method is employed in radio spectral usage in time as the occupancy measurements in the spectrum occupancy measurements, correct determination of three locations were conducted on different days though the the decision threshold upon which a particular channel can same time and days of the week in the same month. The be either deemed free or busy is essential since there is no overall results of the study show that the usage of the radio prior-knowledge about the channel. Hence, according to spectrum in the study locations varies with time, location and [16], correct setting of the threshold metric is important frequency. because high value will lead to under estimation of the Table 1. Decision threshold for each frequency band Frequency band Band Threshold value (dBm) Applications (MHz) Designation Ado-Ekiti Akure Ikeja 80 – 150 A Radio broadcasting band -65.73 -55.63 -54.58 150 – 400 B Television and Land Mobile -53.82 -72.25 -72.24 400 - 960 C Television broadcasting band -69.32 -73.34 -79.12 700 - 1000 D Trunk radio services and GSM band -70.18 -72.46 -78.32 900 - 1300 E GSM band -73.11 -71.22 -75.55 1300- 1700 F Rural Telecoms and GSM bands -65.66 -93.43 -93.13 1700- 1900 G GSM, Oil coy and Satellite broadcast -80.27 -84.63 -86.99 1900- 2200 H 3G band -86.44 -86.26 -94.69 127 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 (i) (i) (ii) (ii) (iii) (iii) Fig. 6. Spectrum occupancy at 80-150 MHz for (i) Ado- Fig. 7. Spectrum occupancy at 400-960 MHz for (i) Ekiti, (ii) Akure and (iii) Ikeja respectively Ado-Ekiti, (ii) Akure and (iii) Ikeja respectively 128 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 (i) (i) (ii) (ii) (iii) (ii) Fig. 8. Spectrum occupancy at 900-1300 MHz for (i) Fig. 9. Spectrum occupancy at 1900-2200 MHz for (i) Ado-Ekiti, (ii) Akure and (iii) Ikeja respectively Ado-Ekiti, (ii) Akure and (iii) Ikeja respectively 129 INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 licensed owner of the spectrum via spectrum trading [19], which according to [21] is the act of selling and buying radio Ado-Ekiti Akure Lagos spectrum in a cognitive radio environment. This economic advantage is feasible under DSA because the flexibility 100 involved permits dynamic spectrum market where PUs or licensed owners lease out their spectrum holes or unused channels to generate revenue whenever their channels are not 10 used. Thus the capability of DSA in converting the unused channel that is currently a waste under the current rigid radio 1 spectrum management to wealth for the PUs or licensed owners is a major economic benefit. 0.1 In addition, another economic advantage of DSA is that it enhances cost effective access. This enables secondary users to use free and leased spectrum as well as usage of 0.01 Band A Band B Band C Band D Band E Band F Band G Band H existing radio towers and other infrastructures. According to Frequency Band [19], this act enables smaller scale and lower entry costs become feasible to drive down the service prices. These Fig. 10. Overall radio spectrum occupancy for each band lower entry costs according to Reference [19] brings about increase in the introduction of new wireless products and Fig.10 shows the overall radio spectral occupancy for services in the marketplace. This cost effective access each band using the band designation used in Table 1. The provides by DSA does not only improve broadband logarithm scale of the actual occupancy rate obtained was communication system but also promote job opportunity as plotted against the frequency band. The logarithm scale was well as contributing to the nation’s economy. Similarly, used on the vertical axis in Fig.10 in order to normalise the according to [22], another economic advantage of DSA is occupancy rate. The results show variation in the usage of that its cost effective access methodology increases faster each frequency band with location. The results also show that entry and exist in the market place as well as driving down while a particular frequency was being heavily utilized in a wireless service prices. This also enhances job creation and particular location the same frequency was being sparingly socio-economic advancement of the nation. utilized in another location. For example, the 80 – 150 MHz frequency band has utilization level of 12.41% in Ado-Ekiti 5. Conclusion while the corresponding values for the frequency band in Akure and Lagos are 16.3% and 0.14% respectively. This Obviously, radio spectrum is a major enabler of wireless shows that Band A is sparingly utilised in Ikeja while the communication systems. As a result of its indispensability in band has medium utilization in Akure and Ado-Ekiti. On the wireless communication systems, radio spectrum is being other hand, the overall result as shown in Fig.10 shows that regulated by both the international and national bodies Bands D, E and H which are GSM bands are heavily utilized worldwide. However, recent observations have shown that in Ikeja while the bands are fairly utilised in Akure and radio spectrum is not effectively and efficiently utilized by sparingly utilised in Ado-Ekiti. Generally, Fig.10 shows that licensed owners under the current fixed radio spectrum the overall spectrum occupancy in the three locations range allocation policy. Specifically, the overall spectrum from 0.08% - 64.4%. This shows that there is availability of occupancy or utilization efficiency obtained in this study that spectrum holes that can be converted from waste to wealth if ranges from 0.08% to 64.4% shows that the current fixed DSA is deployed in the country’s radio spectrum radio spectrum management policy is far overdue and needs management. Recently, according to [20], the radio spectrum to be replaced with flexible management policy that will regulators in the United States and the United Kingdom have improve the utilization of radio spectrum. With the rapid given conditional endorsement to DSA mode of spectrum progress in DSA technology and economic advantages of access based on its economic advantages. This implies that DSA, this paper is recommending the replacement of the adoption of DSA in radio spectrum management policy in current fixed spectrum allocation policy with DSA so that the underdeveloped nation like Nigeria and generally all over the current radio spectrum wastage can be converted to wealth. world has some economic advantages. Another significant contribution of this study is that it One of the economic benefits of DSA is that it enables shows the practical relationship of spectrum occupancy with secondary users of the radio spectrum to utilize the spectrum locations. Unlike most similar studies in surveyed literature holes in an opportunistic manner. It thus enhances the that consider one or two location(s) with few frequency efficiency of spectrum usage as well as helping in eradicating bands, the study presented in this paper was conducted in the current problem of radio spectrum scarcity and three different locations using eight different frequency underutilization. Also, the deployment of the DSA bands. The results of the study show that spectrum technology will enhance the availability of spectral resources occupancy varies from one location to another. Finally, as a for future emerging wireless services, devices and way of concluding this paper, it is obvious that the applications [19]. Apart from the fact that DSA can enhance replacement of the current fixed or rigid radio spectrum spectral utilization efficiency, another economic advantage management policy with DSA will not only convert the of DSA is that it also provides extra revenue for the PU or current radio spectrum wastage to wealth and enhancing 130 Ocupancy Rate (%) INTERNATIONAL JOURNAL of ENGINEERING TECHNOLOGIES Jide J. Popoola et al., Vol.2, No.3, 2016 radio spectrum management and its utilization, but will also [11] J.J. Popoola, R. Van Olst, (2011) “Application of neural not compromise the performance of the existing radio being network for sensing primary radio signals in a cognitive governed by the fixed spectrum allocation policy. radio environment”, Proc. of IEEE AFRICON, Livingstone, Zambia, September 13 – 15, pp. 1-6. Acknowledgements [12] M. Chiani, A. Giorgetti, G. Liva, (2005) “Ultra wide bandwidth communications towards cognitive radio”, Authors thank Akinlolu Ponnle of Department of Proc. 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Article Template Containing Author Guidelines for Peer-Review First Author*, Second Author**‡, Third Author*** *Department of First Author, Faculty of First Author, Affiliation of First Author, Postal address **Department of Second Author, Faculty of First Author, Affiliation of First Author, Postal address ***Department of Third Author, Faculty of First Author, Affiliation of First Author, Postal address (First Author Mail Address, Second Author Mail Address, Third Author Mail Address) ‡ Corresponding Author; Second Author, Postal address, Tel: +90 312 123 4567, Fax: +90 312 123 4567,corresponding@affl.edu Received: xx.xx.xxxx Accepted:xx.xx.xxxx Abstract- Enter an abstract of up to 250 words for all articles. This is a concise summary of the whole paper, not just the conclusions, and is understandable without reference to the rest of the paper. It should contain no citation to other published work. Include up to six keywords that describe your paper for indexing purposes. Define abbreviations and acronyms the first time they are used in the text, even if they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, sc, dc, and rms do not have to be defined. Do not use abbreviations in the title unless they are unavoidable. Keywords- Keyword1; keyword2; keyword3; keyword4; keyword5. 2. Introduction Authors should any word processing software that is capable to make corrections on misspelled words and grammar structure according to American or Native English. Authors may get help by from word processor by making appeared the paragraph marks and other hidden formatting symbols. This sample article is prepared to assist authors preparing their articles to IJET. Indent level of paragraphs should be 0.63 cm (0.24 in) in the text of article. Use single column layout, double-spacing and wide (3 cm) margins on white paper at the peer review stage. Ensure that each new paragraph is clearly indicated. Present tables and figure legends in the text where they are related and cited. Number all pages consecutively; use 12 pt font size and standard fonts; Times New Roman, Helvetica, or Courier is preferred. Indicate references by number(s) in square brackets in line with the text. The actual authors can be referred to, but the reference number(s) must always be given. Example: "..... as demonstrated [3, 6]. Barnaby and Jones [8] obtained a different result ...." IJET accepts submissions in three styles that are defined as Research Papers, Technical Notes and Letter, and Review paper. The requirements of paper are as listed below:  Research Papers should not exceed 12 printed pages in two-column publishing format, including figures and tables.  Technical Notes and Letters should not exceed 2,000 words.  Reviews should not exceed 20 printed pages in two-column publishing format, including figures and tables. Authors are requested write equations using either any mathematical equation object inserted to word processor or using independent equation software. Symbols in your equation should be defined before the equation appears or immediately following. Use “Eq. (1)” or “equation (1),” while citing. Number equations consecutively with equation numbers in parentheses flush with the right margin, as in Eq. (1). To make equations more compact, you may use the solidus ( / ), the exp function, or appropriate exponents. Italicize Roman symbols for quantities and variables, but not Greek symbols. Use an dash (–) rather than a hyphen for a minus sign. Use parentheses to avoid ambiguities in denominators. Punctuate equations with commas or periods when they are part of a sentence, as in C = a + b (1) Section titles should be written in bold style while sub section titles are italic. 3. Figures and Tables 3.1. Figure Properties All illustrations must be supplied at the correct resolution:  Black and white and colour photos - 300 dpi  Graphs, drawings, etc - 800 dpi preferred; 600 dpi minimum  Combinations of photos and drawings (black and white and colour) - 500 dpi In addition to using figures in the text, Authors are requested to upload each figure as a separate file in either .tiff or .eps format during submission, with the figure number as Fig.1., Fig.2a and so on. Figures are cited as “Fig.1” in sentences or as “Figure 1” at the beginning of sentence and paragraphs. Explanations related to figures should be given before figure. Figures and tables should be located at the top or bottom side of paper as done in accepted article format. Figure 1. Engineering technologies. Table captions should be written in the same format as figure captions; for example, “Table 1. Appearance styles.”. Tables should be referenced in the text unabbreviated as “Table 1.” Table 1. Appearance properties of accepted manuscripts Type size Appearance (pts.) Regular Bold Italic 10 Authors’ affiliations, Abstract, keywords, Abstract references, tables, table names, figure captions, footnotes, text subscripts, and superscripts 12 Main text, equations, Authors’ names, Subheading Section titles (1.1.) 24 Paper title 4. Submission Process The International Journal of Engineering Technologies operates an online submission and peer review system that allows authors to submit articles online and track their progress via a web interface. Articles that are prepared referring to this template should be controlled according to submission checklist given in “Guide f Authors”. Editor handles submitted articles to IJET primarily in order to control in terms of compatibility to aims and scope of Journal. Articles passed this control are checked for grammatical and template structures. If article passes this control too, then reviewers are assigned to article and Editor gives a reference number to paper. Authors registered to online submission system can track all these phases. Editor also informs authors about processes of submitted article by e-mail. Each author may also apply to Editor via online submission system to review papers related to their study areas. Peer review is a critical element of publication, and one of the major cornerstones of the scientific process. Peer Review serves two key functions:  Acts as a filter: Ensures research is properly verified before being published  Improves the quality of the research 5. Conclusion The conclusion section should emphasize the main contribution of the article to literature. Authors may also explain why the work is important, what are the novelties or possible applications and extensions. Do not replicate the abstract or sentences given in main text as the conclusion. Acknowledgements Authors may acknowledge to any person, institution or department that supported to any part of study. References [1] J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford:Clarendon Press, 1892, pp.68-73. (Book) [2] H. Poor, An Introduction to Signal Detection and Estimation, New York: Springer-Verlag, 1985, ch. 4. (Book Chapter) [3] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, “Electron spectroscopy studies on magneto-optical media and plastic substrate interface”, IEEE Transl. J. Magn. Japan, vol. 2, pp. 740-741, August 1987. (Article) [4] E. Kabalcı, E. Irmak, I. Çolak, “Design of an AC-DC-AC converter for wind turbines”, International Journal of Energy Research, Wiley Interscience, DOI: 10.1002/er.1770, Vol. 36, No. 2, pp. 169-175. (Article) [5] I. Çolak, E. Kabalci, R. Bayindir R., and S. Sagiroglu, “The design and analysis of a 5-level cascaded voltage source inverter with low THD”, 2nd PowerEng Conference, Lisbon, pp. 575-580, 18-20 March 2009. (Conference Paper) [6] IEEE Standard 519-1992, Recommended practices and requirements for harmonic control in electrical power systems, The Institute of Electrical and Electronics Engineers, 1993. (Standards and Reports) Article Template Containing Author Guidelines for Accepted Papers First Author*, Second Author**‡, Third Author*** *Department of First Author, Faculty of First Author, Affiliation of First Author, Postal address **Department of Second Author, Faculty of First Author, Affiliation of First Author, Postal address ***Department of Third Author, Faculty of First Author, Affiliation of First Author, Postal address (First Author Mail Address, Second Author Mail Address, Third Author Mail Address) ‡ Corresponding Author; Second Author, Postal address, Tel: +90 312 123 4567, Fax: +90 312 123 4567,corresponding@affl.edu Received: xx.xx.xxxx Accepted:xx.xx.xxxx Abstract- Enter an abstract of up to 250 words for all articles. This is a concise summary of the whole paper, not just the conclusions, and is understandable without reference to the rest of the paper. It should contain no citation to other published work. Include up to six keywords that describe your paper for indexing purposes. Define abbreviations and acronyms the first time they are used in the text, even if they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, sc, dc, and rms do not have to be defined. Do not use abbreviations in the title unless they are unavoidable. Keywords Keyword1, keyword2, keyword3, keyword4, keyword5. 1. Introduction  Research Papers should not exceed 12 printed pages in two-column publishing format, including figures and Authors should any word processing software that is tables. capable to make corrections on misspelled words and grammar structure according to American or Native English.  Technical Notes and Letters should not exceed Authors may get help by from word processor by making 2,000 words. appeared the paragraph marks and other hidden formatting  Reviews should not exceed 20 printed pages in two- symbols. This sample article is prepared to assist authors column publishing format, including figures and tables. preparing their articles to IJET. Authors are requested write equations using either any Indent level of paragraphs should be 0.63 cm (0.24 in) in mathematical equation object inserted to word processor or the text of article. Use single column layout, double-spacing using independent equation software. Symbols in your and wide (3 cm) margins on white paper at the peer review equation should be defined before the equation appears or stage. Ensure that each new paragraph is clearly indicated. immediately following. Use “Eq. (1)” or “equation (1),” Present tables and figure legends in the text where they are while citing. Number equations consecutively with equation related and cited. Number all pages consecutively; use 12 pt numbers in parentheses flush with the right margin, as in Eq. font size and standard fonts; Times New Roman, Helvetica, (1). To make equations more compact, you may use the or Courier is preferred. Indicate references by number(s) in solidus ( / ), the exp function, or appropriate exponents. square brackets in line with the text. The actual authors can Italicize Roman symbols for quantities and variables, but not be referred to, but the reference number(s) must always be Greek symbols. Use an dash (-) rather than a hyphen for a given. Example: "..... as demonstrated [3,6]. Barnaby and minus sign. Use parentheses to avoid ambiguities in Jones [8] obtained a different result ...." denominators. Punctuate equations with commas or periods IJET accepts submissions in three styles that are defined when they are part of a sentence, as in as Research Papers, Technical Notes and Letter, and Review C = a + b (1) paper. The requirements of paper are as listed below: Section titles should be written in bold style while sub section titles are italic. 6. Figures and Tables 6.1. Figure Properties All illustrations must be supplied at the correct resolution:  Black and white and colour photos - 300 dpi  Graphs, drawings, etc - 800 dpi preferred; 600 dpi minimum  Combinations of photos and drawings (black and white and colour) - 500 dpi Fig. 1. Engineering technologies. In addition to using figures in the text, Authors are Figures and tables should be located at the top or bottom requested to upload each figure as a separate file in either side of paper as done in accepted article format. Table .tiff or .eps format during submission, with the figure number captions should be written in the same format as figure as Fig.1., Fig.2a and so on. Figures are cited as “Fig.1” in captions; for example, “Table 1. Appearance styles.”. Tables sentences or as “Figure 1” at the beginning of sentence and should be referenced in the text unabbreviated as “Table 1.” paragraphs. Explanations related to figures should be given before figure. Table 1. Appearance properties of accepted manuscripts Appearance Type size (pts.) Regular Bold Italic Main text, section titles, authors’ affiliations, abstract, 10 keywords, references, tables, table names, figure captions, Abstract- Subheading (1.1.) equations, footnotes, text subscripts, and superscripts 12 Authors’ names, 24 Paper title 6.2. Text Layout for Accepted Papers progress via a web interface. Articles that are prepared referring to this template should be controlled according to A4 page margins should be margins: top = 24 mm, submission checklist given in “Guide f Authors”. Editor bottom = 24 mm, side = 15 mm. The column width is 87mm handles submitted articles to IJET primarily in order to (3.425 in). The space between the two columns is 6 mm control in terms of compatibility to aims and scope of (0.236 in). Paragraph indentation is 3.5 mm (0.137 in). Journal. Articles passed this control are checked for Follow the type sizes specified in Table. Position figures and grammatical and template structures. If article passes this tables at the tops and bottoms of columns. Avoid placing control too, then reviewers are assigned to article and Editor them in the middle of columns. Large figures and tables may gives a reference number to paper. Authors registered to span across both columns. Figure captions should be centred online submission system can track all these phases. Editor also informs authors about processes of submitted article by below the figures; table captions should be centred above. Avoid placing figures and tables before their first mention in e-mail. Each author may also apply to Editor via online the text. Use the abbreviation “Fig. 1,” even at the beginning submission system to review papers related to their study of a sentence. areas. Peer review is a critical element of publication, and one of the major cornerstones of the scientific process. Peer Review serves two key functions: 7. Submission Process  Acts as a filter: Ensures research is properly verified The International Journal of Engineering Technologies before being published operates an online submission and peer review system that  Improves the quality of the research allows authors to submit articles online and track their 8. Conclusion The conclusion section should emphasize the main contribution of the article to literature. Authors may also explain why the work is important, what are the novelties or possible applications and extensions. Do not replicate the abstract or sentences given in main text as the conclusion. Acknowledgements Authors may acknowledge to any person, institution or department that supported to any part of study. References [7] J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford:Clarendon Press, 1892, pp.68-73. (Book) [8] H. Poor, An Introduction to Signal Detection and Estimation, New York: Springer-Verlag, 1985, ch. 4. (Book Chapter) [9] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, “Electron spectroscopy studies on magneto-optical media and plastic substrate interface”, IEEE Transl. J. Magn. Japan, vol. 2, pp. 740-741, August 1987. (Article) [10] E. Kabalcı, E. Irmak, I. Çolak, “Design of an AC- DC-AC converter for wind turbines”, International Journal of Energy Research, Wiley Interscience, DOI: 10.1002/er.1770, Vol. 36, No. 2, pp. 169-175. (Article) [11] I. Çolak, E. Kabalci, R. Bayindir R., and S. Sagiroglu, “The design and analysis of a 5-level cascaded voltage source inverter with low THD”, 2nd PowerEng Conference, Lisbon, pp. 575-580, 18-20 March 2009. (Conference Paper) [12] IEEE Standard 519-1992, Recommended practices and requirements for harmonic control in electrical power systems, The Institute of Electrical and Electronics Engineers, 1993. (Standards and Reports) INTERNATIONAL JOURNAL OF ENGINEERING TECHNOLOGIES (IJET) COPYRIGHT AND CONSENT FORM This form is used for article accepted to be published by the IJET. Please read the form carefully and keep a copy for your files. TITLE OF ARTICLE (hereinafter, "The Article"): ………..…………………………………………………....................………………………………………………………… ………..…………………………………………………....................…………………………………………………………… …………..………………………………………………………………………..…………………………………………… LIST OF AUTHORS: ………..……………………………………………………………...…..……………………………………………………… ………..…………………………………………………....................…………………………………………………………… ……………………………………………………………………..……………………………………………..…………… CORRESPONDING AUTHOR’S (“The Author”) NAME, ADDRESS, INSTITUTE AND EMAIL: ………………………………………………………………………..………………………………………………………… ………..…………………………………………………....................…………………………………………………………… …………..………………………………………………………………………..…………………………………….…… COPYRIGHT TRANSFER The undersigned hereby transfers the copyright of the submitted article to International Journal of Engineering Technologies (the "IJET"). The Author declares that the contribution and work is original, and he/she is authorized by all authors and/or grant-funding agency to sign the copyright form. Author hereby assigns all including but not limited to the rights to publish, distribute, reprints, translates, electronic and published derivates in various arrangements or any other versions in full or abridged forms to IJET. IJET holds the copyright of Article in its own name. Author(s) retain all rights to use author copy in his/her educational activities, own websites, institutional and/or funder’s web sites by providing full citation to final version published in IJET. The full citation is provided including Authors list, title of the article, volume and issue number, and page number or using a link to the article in IJET web site. Author(s) have the right to transmit, print and share the first submitted copies with colleagues. Author(s) can use the final published article for his/her own professional positions, career or qualifications by citing to the IJET publication. Once the copyright form is signed, any changes about the author names or order of the authors listed above are not accepted by IJET. Authorized/Corresponding Author Date/ Signature