Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation

The nonlinear vibration and the dynamic buckling of a graphene platelet reinforced sandwich functionally graded porous (GPL-SFGP) plate are thoroughly investigated in this paper. The investigated GPL-SFGP plate consists of two metal face layers and a functionally graded porous core with graphene platelet reinforcement. The effects of the Winkler-Pastemak elastic foundation, thermal environment and damping are incorporated. The open-cell metal foam model is implemented to model the mechanical properties of the porous core. Axial compressive stress is applied on the GPL-SFGP plate by exerting various compressive loading speeds at one edge of the plate. Grounded on the classical plate theory, both motion and geometric compatibility equations of the plate are deduced by introducing the Von Karman strain-displacement relationship and stress function. Both the Galerkin and the fourth-order Runge-Kutta methods are implemented to solve the governing equation of the dynamic system. Meticulously designed numerical experiments are conducted to identify the critical influential factors of the dynamic stability of the GPL-SFGP plate. The influences of loading speed, damping ratio, temperature variation, initial imperfection, elastic foundation parameters, porosity, GPL weight fraction and the dimensions of the GPL on the overall dynamic stability of the GPL-SFGP plate are evidently demonstrated.