Nonlinear electro-mechanical coupling vibration of corrugated graphene/piezoelectric laminated structures

Abstract

An analytical method is presented to investigate the nonlinear dynamic behavior of corrugated graphene/piezoelectric (CGP) laminated structures under electro-mechanical coupling loads, where the corrugated graphene is affixed on a piezoelectric film. An equivalent orthotropic plate method is used to obtain the stiffness coefficients of corrugated graphene sheet, and its accuracy is validated by the finite element method (FEM). The nonlinear dynamic governing equations of CGP laminated films are constructed based on von Kármán nonlinear geometric relations, then is solved by the Galerkin method and iterative homotopy harmonic balance method. Results show that the equivalent orthotropic plate method is reliable in analyzing the resonant frequency of corrugated film, and both geometry nonlinearity and external control voltage exerted on piezoelectric film have significant effects on the dynamic behaviors of CGP laminated films. Additionally, though corrugated graphene sheet exhibits smaller material stiffness, a significant effect on resonant frequency is observed by affixing corrugated graphene on piezoelectric plate. The meaningful results could serve as references for the applications of soft super-capacitors, stretchable electrode devices, nano-sensors, and etc.