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Öğe Influences of material gradient and nonlinearity on the forced vibration of orthotropic shell structures(ELSEVIER SCI LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, OXON, ENGLAND, 2021) Sofiyev, Abdullah H.; Turan, Ferruh; Kuruoğlu, NuriIn this study, the influences of material gradient and nonlinearity on the forced vibration of orthotropic shell structures under external excitations are investigated for first time. The mathematical model of inhomogeneous orthotropic double?curved shallow shells is built using the Hamilton principle and von Karman?type nonlinearity. The basic equations are reduced to nonlinear ordinary differential equations using the Galerkin procedure. Using the multiscale method, the frequency?amplitude relations of double?curved shallow shells and the nonlinear frequency response of forced vibrations are obtained for first time. The reliability of the obtained expressions is checked by comparison with the literature data. In numerical analysis, the influence of inhomogeneity, orthotropy, nonlinearity, and the external excitation parameter on the frequency of forced vibrations is investigated in detail by performing unique numerical calculations taking into account various profiles of inhomogeneous orthotropic shallow spherical and hyperbolic paraboloidal (or hypar) shells.Öğe On the primary resonance of non-homogeneous orthotropic structures with viscous damping within shear deformation theory(ELSEVIER SCI LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, OXON, ENGLAND, 2022) Sofiyev, Abdullah H.; Turan, Ferruh; Kuruoğlu, NuriThis study is one of the first attempts on the nonlinear forced vibration behaviors of nonhomogeneous orthotropic (NHO) structural members with linear viscous damping at primary resonance within the shear deformation theory (SDT). First, mechanical properties of double curved systems consisting of NHO materials are mathematically modeled and nonlinear basic relations are established. Using these relations, nonlinear basic partial differential equations are derived and reduced to ordinary differential equations with second and third order nonlinearities by Galerkin procedure. Multiple-scales method is used to obtain the nonlinear forced vibration frequency–amplitude dependence of double curved NHO structural members with damping. After testing the correctness of the proposed methodology, the influences of non-homogeneity, damping, transverse shear deformations and anisotropy on nonlinear forced vibration frequencies for various structural members at the primary resonance are investigated and interpreted in detail.