Nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates subjected to a mechanical shock

The nonlinear frequency response of graphene/piezoelectric sandwich nanoplates under the electric voltage exerted on piezoelectric layer and a shock force pulse is the objective of the present paper. First, using von Karman nonlinear relations, Kelvin–Voigt model, piezoelectric nonlocal elasticity theory and Hamilton's principle, the nonlinear governing differential equation of motion is derived. In the second step, to transform the partial differential equations to the ordinary differential ones, Galerkin technique is employed. Then, governing equation is solved based on multiple scale method. At the end, modulation equation of graphene/piezoelectric sandwich nanoplate is obtained. Emphasizing the effect of the electric voltage and the shock force pulse, the results for fundamental frequency response are obtained. The results emphasize that the exciting loads can cause multivaluedness in frequency response and intensify the jump phenomenon. Also, they can be effective to amplify the vibration behavior of the structure to make resonance. In addition, the thickness of piezoelectric layer plays a significant role in nonlinear frequency response.