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Öğe Mathematical modeling and solution of nonlinear vibration problem of laminated plates with CNT originating layers interacting with two-parameter elastic foundation(Springer Science and Business Media Deutschland GmbH, 2023) Avey M.; Kadıoğlu, F.; Ahmetolan, S.; Fantuzzi, N.Generalizing the first-order shear deformation plate theory (FOPT) proposed by Ambartsumyan (Theory of anisotropic plates, Nauka, Moscow, 1967 (in Russian)) to the heterogeneous laminated nanocomposite plates and the nonlinear vibration problem is analytically solved taking into account an elastic medium in this study for the first time. The Pasternak-type elastic foundation model (PT-EF) is used as the elastic medium model. After creating the mathematical models of laminated rectangular plates with CNT originating layers on the PT-EF, the large amplitude stress–strain relationships and motion equations are derived in the form of nonlinear partial differential equations (PDEs) within FOPT. Then, by applying Galerkin's method to the derived equations, it is reduced to a nonlinear ordinary differential equation (NL-ODE) containing the second- and third-order nonlinear terms of the deflection function for laminated rectangular plates composed of nanocomposite layers. The NL-ODE is solved by the semi-inverse method, and the nonlinear frequency–amplitude relationship for the laminated plates consisting of CNT originating layers resting on the PT-EF is established within FOPT for the first time. From these relations, similar relations can be obtained particularly for the unconstrained laminated and monolayer CNT patterns plates. After comparing the accuracy of the obtained formulas with the reliable results in the literature, comprehensive numerical analyses are performed.Öğe On the primary resonance of laminated moderately-thick plates containing of heterogeneous nanocomposite layers considering nonlinearity(Elsevier, 2023) Avey M.; Kadioglu F.In this study, the primary resonance of laminated plates consisting of heterogeneous nanocomposite layers is investigated comparatively within first order shear deformation theory (FSDT) and classical lamination plate theory (CLPT). One of the features of the work is the generalization of the FSDT for homogeneous anisotropic laminated plates to laminated functionally graded anisotropic nanocomposite plates. The mechanical properties of the matrix reinforced with carbon nanotube (CNT), and fundamental relations of laminated moderately thick plates consisting of heterogeneous anisotropic nanocomposite layers are modeled theoretically within FSDT using von K´ arman ´ type nonlinear theory. It then derives equations of motion in the form of nonlinear partial differential equations (NL-PDEs) within FSDT. NL-PDEs equations are transformed into nonlinear ordinary dif ferential equations (NL-ODEs) by Galerkin method and are solved by multi-scale method. The nonlinear forced vibration frequency as the function of amplitude at primary resonance within both theories are obtained for the first time. In addition, backbone curve and nonlinear frequency/linear frequency ratio are found. The reliability and accuracy of the proposed formulation is verified by comparing with the results in the literature. Finally, the effects of external excitation, non-linearity, and variation of CNT patterns on the forced vibration frequencies are examined.Öğe Thermoelastic stability of CNT patterned conical shells under thermal loading in the framework of shear deformation theory(Taylor and Francis Ltd., 2022) Avey M.; Fantuzzi N.; Sofiyev A.H.This study presents the thermoelastic stability of carbon nanotube (CNT) patterned composite conical shells in the framework of shear deformation theory (ST). The study includes two different boundary value problems. As the material properties are independent of temperature, the truncated conical shell is assumed to be under thermal load, and when the material properties are temperature dependent, the conical shell is assumed to be under axial compressive load. The modified Donnell-type shell theory is used to derive the basic equations for CNT patterned truncated conical shells. The Galerkin method is applied to the basic equations to find the critical temperature and critical axial load expressions of CNT patterned composite truncated conical shells in the framework of ST. The effect of changes in CNT patterns, volume fraction, radius-to-thickness and length-to-thickness ratios, as well as the half-peak angle on critical parameters within the ST, are estimated by comparison with classical shell theory (CT).Öğe Vibration of laminated functionally graded nanocomposite structures considering the transverse shear stresses and rotary inertia(Elsevier Ltd, 2022) Avey M.; Fantuzzi N.; Sofiyev A.H.The aim of this study is to determine the fundamental frequencies of laminated double-curved nanocomposite structures considering transverse shear stresses (TSSs) and rotary inertia (RI). The basic equations of laminated double-curved structures composed of CNT patterned layers based on the Donnell type shell theory are derived within TSSs and considering RI. By applying the Galerkin technique, the fundamental equations are transformed into frequency-dependent sixth-order algebraic equations, and this equation is solved numerically to find the fundamental frequency for laminated double curved structures consisting of CNT patterned layers considering TSSs and RI. In addition, when the rotary inertia is neglected, analytical expressions for frequencies are obtained in the framework of shear deformation theory (ST) and classical theory (CT). Finally, the influences of the volume fraction, CNT patterns, array of nanocomposite layers, TSSs and RI on the fundamental frequency are examined.
