Nonlinear dynamic analysis of composite piezoelectric plates with graphene skin

This paper studies the nonlinear dynamical characteristic of a composite plate made of new three-phase materials which include the graphene (GP) combined with macro fiber composite (MFC) in the polymer. The GP is supposed to be uniformly dispersed in the upper and lower surfaces of the composite laminated plate with 1-3 mode of macro fiber. The cross-ply MFC composite laminated plate is subjected to transversal excitations. The constitutive laws for the MFC-GP composite material are obtained based on the rule of mixture for multi-components of composite material. The nonlinear governing equations of motion of the MFC-GP plate are derived by Hamilton's principle and the von Kármán geometrical kinematics. Galerkin's approach is employed to discretize the partial differential governing equations into a two-degree-of-freedom nonlinear system. Then, stability analysis is conducted to investigate the influences of various parameters on natural frequencies of the MFC-GP plate, with a particular focus on the effects of GP volume fraction, initial conditions and damping coefficients on nonlinear vibration behaviours of the composite plate.