▎ 摘　　要

This paper presents a unified higher-order shear deformable plate model to numerically examine the nonlinear vibration behavior of thick and moderately thick polymer nanocomposite rectangular plates reinforced by graphene platelets (GPLs). Four distribution patterns of graphene nanoplatelet nanofillers across the plate thickness are considered. The effective material properties of graphene platelet-reinforced polymer (GPL-RP) nanocomposite plate are approximately calculated by employing the modified Halpin-Tsai model and rule of mixture. Using a generalized displacement field, a unified mathematical formulation is derived based on Hamilton's principle in conjunction with von Karman geometrical nonlinearity. By selecting appropriate shape functions, the proposed unified nonlinear plate model can be reduced to that on the basis of Mindlin, Reddy, parabolic, trigonometric and exponential shear deformation plate theories. The investigation of nonlinear vibration behavior is performed by employing a multistep numerical solution approach. In this regard, the discretization process is done through the generalized differential quadrature method. Then, the discretized governing equations are solved by employing the numerical-based Galerkin technique, periodic time differential operators and pseudo-arc length continuation algorithm. A detailed parametric study is carried out to examine the effect of GPL distribution pattern, weight fraction, geometry of GPL nanofillers and boundary constraints on the nonlinear vibration characteristics of the GPL-RP nanocomposite rectangular plates.