Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments

This paper deals with the large amplitude vibration of functionally graded graphene-reinforced composite laminated plates resting on an elastic foundation and in thermal environments. The temperature-dependent material properties of piece-wise functionally graded graphene-reinforced composites (FG-GRCs) are assumed to be graded in the thickness direction of a plate, and are estimated through a micromechanical model. Based on a higher-order shear deformation plate theory, the motion equations are developed with geometric nonlinearity taking the form of von Kármán strains. The plate-foundation interaction and thermal effects are also included. The motion equations are then solved by a two-step perturbation technique to determine the nonlinear frequencies of the FG-GRC laminated plates. The numerical illustrations concern the nonlinear vibration characteristics of FG-GRC laminated plates under different sets of thermal environmental conditions, from which results for uniformly distributed GRC laminated plates are obtained as comparators. The effects of distribution type of reinforcements, temperature variation, foundation stiffness and different in-plane boundary conditions are also investigated.