On the primary resonance of laminated moderately-thick plates containing of heterogeneous nanocomposite layers considering nonlinearity

Abstract

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 Kármán 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 differential 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.