Nonlinear dynamics analysis of a graphene laminated composite plate based on an extended Rayleigh-Ritz method

Linear and nonlinear vibration characteristics of the graphene platelet-reinforced composite (GPLRC) laminated plates are investigated. Based on the first-order shear theory and von Karman geometric nonlinearity, the energy expressions of the GPLRC laminates are established. The boundary elastic potential energy is established by penalty function method to simulate different boundary conditions. The linear and nonlinear frequencies of the GPLRC laminated plate are calculated by introducing boundary potential energy into Rayleigh-Ritz method. The convergence and accuracy of the method are verified by numerical examples, and the effects of different parameters on frequency are analyzed. Considering the cantilever boundary conditions, the nonlinear motion governing equations of the GPLRC laminated plate are obtained by Hamilton principle. The two-degree -freedom ordinary differential motion equations of the laminates are derived by Galerkin method. Considering the fundamental parameter resonance and 1:1 internal resonance, the amplitude-frequency response curves of the structure under transverse excitation are obtained. The effects of transverse excitation and damping coefficient on nonlinear vibration characteristics of the GPLRC laminated plates are investigated by numerical simulation.