Nonlinear forced vibration of FG-GRC laminated plates resting on visco-Pasternak foundations

The nonlinear dynamic responses of laminated plates consisting of graphene reinforced composite (GRC) layers in thermal environments are studied in this paper. The effect of visco-elastic foundation is also considered in the analysis. All layers in an FG-GRC laminated plate are assumed to have the same thickness, whereas the graphene volume fractions for the layers are assumed to be linearly varying in a piece-wise pattern along the plate thickness direction. The material properties of GRC are estimated by a extended Halpin-Tsai model. To include the effect of small scale, the efficiency parameters for graphene are introduced in the model and determined from the results of molecular dynamics (MD) simulations. The plate is modeled based on the Reddy's higher order shear deformation plate theory and the effects of the von Karman geometric nonlinearity and the initial loading are included in the derivation of the motion equations. Once the applied load is determined, the deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. The impacts of functionally graded (FG) pattern, visco-elastic foundations, temperature change and applied load type on the dynamic behaviors of the FG-GRC plate are presented and discussed.