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    An efficient approach for free vibration analysis of functionally graded sandwich beams of variable cross-section
    (Elsevier Science Inc, 2023) Aslan, Timucin Alp; Noori, Ahmad Reshad; Temel, Beytullah
    In this research paper, a powerful numerical method is implemented to examine the free vibration analysis of functionally graded (FG) sandwich beams of variable cross-section. The core of the beam is considered to be made from homogenous isotropic material and the faces of the sandwich beam are considered to be made of FG materials. The effect of the shear strain is considered in the formulations based on the first-order shear deformation theory (FSDT). The governing canonical equations for the dynamic response of FG sandwich beams are derived with the aid of the canonically conjugate momentums for the first time. To solve these equations numerically the Complementary Functions Method (CFM) is implemented. The free vibration behavior of the symmetric and asymmetric FG sandwich beams is investigated for different boundary conditions. The presented efficient numerical method is validated with the available literature. Moreover, detailed parametric studies are conducted to demonstrate the influence of layers, geometric constants, material volume fraction indexes, and beam slenderness on the natural frequencies of FG sandwich beams.
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    In-plane vibration analysis of parabolic arches having a variable thickness
    (Springernature, 2021) Temel, Beytullah; Aslan, Timucin Alp; Noori, Ahmad Reshad
    This article deals with free and forced vibration responses of the viscoelastic parabolic arches of variable thickness. Firstly, considering the effects of shear deformation and damping, time-dependent motion equations of in-plane loaded parabolic arches are obtained. Subsequently, the Laplace transform is applied to the obtained equations and solved by a powerful numerical method. Furthermore, the Kelvin viscose model is used to describe the viscoelastic material. Using an effective and suitable inverse numerical Laplace transform method, the results were transferred back to time space. The verification of the presented method is performed by comparing its results with the results of ANSYS. It has been shown in several examples that the proposed method is highly accurate and efficient compared to step-by-step time integration methods.