Nonlinear dynamic modeling of smart graphene/piezoelectric composite nanoplates subjected to dual frequency excitation

Abstract

The nonlinear frequency response of graphene/PZT/graphene nano composite subjected to multi-frequency excitation is the objective of this paper. The nano composite is embedded on a visco-Pasternak foundation. Firstly, based on the nonlocal continuum theory and nonlinear von Karman strain-displacement relations, the nonlinear governing differential equation of motion is derived. Secondly, the Galerkin method is employed to transfer the partial differential equation to the ordinary differential equation. Then, the governing equation is solved based on the multiple time scales method. It is demonstrated that the multiple time scales is a useful analytical method to analyze nonlinear problems. Finally, the modulation equation under sub-harmonic and super-harmonic stimulation is studied. Emphasizing the influence of nonlinearity and dual frequency excitation, the nonlinear frequency response, phase angle and amplitude response of graphene/PZT/graphene nano composite are discussed. At the end, the numerical results are performed while the emphasis is placed on investigating the effect of nonlocal parameter, damping coefficient, multi-frequency external excitation, electric voltage load and visco-Pasternak foundation coefficients of the graphene/PZT/graphene nano composite. The results illustrate that dual frequency excitation can intensify the nonlinear frequency response. In addition, the electric voltage as well as external excitation plays an important role in resonance phenomenon.