Influence of nonlinear terms on dynamical behavior of graphene reinforced laminated composite plates

•Nonlinear governing equations of a 5-ply graphene reinforced laminated composite plate are built.•The effects of nonlinear terms on dynamical behavior of the graphene laminated plate is investigated.•Both the cases of stronger and weaker nonlinear characteristic are compared and verified.•The influence mechanism of the nonlinear characteristic on dynamics of the plate is discussed.