A novel technique for nonlinear dynamic instability analysis of FG-GRC laminated plates

This paper presents a novel technique for the nonlinear dynamic instability analysis of graphene-reinforced composite (GRC) laminated plates resting on an elastic foundation and in thermal environments. The GRC layers are arranged in a piece-wise functionally graded (FG) pattern along the plate thickness direction and each layer of the plate contains different volume fractions of graphene reinforcement. The material properties of a GRC layer are assumed to be temperature-dependent and are estimated by the extended Halpin-Tsai micromechanical model. The governing equations are based on a higher-order shear deformation plate theory with the geometric nonlinearity being defined by the von Karman strain-displacement relationships. The plate-foundation interaction and thermal effects are also included. The novelty of this study is that the motion equation and the post-buckling equilibrium equation are derived by a two-step perturbation technique and are then solved simultaneously to determine the dynamic in-plane load and frequency uniquely for a given plate amplitude. The numerical illustrations reveal the nonlinear dynamic instability responses of FG-GRC laminated plates under different sets of thermal environmental conditions, from which results for uniformly distributed (UD) GRC laminated plates are obtained as comparators.