Nonlinear stability and vibration of pre/post-buckled multilayer FG-GPLRPC rectangular plates

Abstract

• Proposing the nonlinear equations of parabolic shear deformable FG-GPLRPC plates. • Prediction of nonlinear stability and vibration of pre- and post-buckled FG-GPLRPC plates. • Investigating the impacts of GPL distribution scheme and weight fraction. • Exploring the impacts of the GPLs’ and plate's geometry and boundary conditions. The present study examines the nonlinear stability and free vibration features of multilayer functionally graded graphene platelet-reinforced polymer composite (FG-GPLRPC) rectangular plates under compressive in-plane mechanical loads in pre/post buckling regimes. The GPL weight fractions layer-wisely vary across the lateral direction. Furthermore, GPLs are uniformly dispersed in the polymer matrix of each layer. The effective Young's modulus of GPL-reinforced nanocomposite is assessed via the modified Halpin–Tsai technique, while the effective mass density and Poisson's ratio are attained by the rule of mixture. Taking the von Kármán-type nonlinearity into account for the large deflection of the FG-GPLRPC plate, as well as utilizing the variational differential quadrature (VDQ) method and Lagrange equation, the system of discretized coupled nonlinear equations of motions is directly achieved based upon a parabolic shear deformation plate theory; taking into account the impacts of geometric nonlinearity, in-plane loading, rotary inertia and transverse shear deformation. Afterwards, first, by neglecting the inertia terms, the pseudo-arc length approach is used in order to plot the equilibrium postbuckling path of FG-GPLRPC plates. Then, supposing a time-dependent disturbance about the postbuckling equilibrium status, the frequency responses of pre/post-buckled FG-GPLRC plate are obtained in terms of the compressive in-plane load. The influences of various vital design parameters are discussed through various parametric studies.