Nonlinear vibrations of graphene piezoelectric microsheet under coupled excitations

Abstract

Investigated herein are the nonlinear vibration characteristics of a rectangular microsheet comprising micro fiber composite with graphene (GP) skin under coupled excitations. Owing to the good thermal conductivity of GP, the heat sink performance of the GP skin is also considered. In this study, the constitutive relation for the microsheet is established by applying the Eringen theory and the governing equations for nonlinear dynamics of the microsheet are obtained from the principle of conservation of energy. The Green and Naghdi’s generalized thermo-elasticity theory and the Galerkin weighted residual method are employed to describe the thermo-elasticity coupling effect of the MFC-GP microsheet. The positive piezoelectric effects of graphene and MFC are also taken into consideration. Next, the coupled ordinary differential equations of thermo-elasticity-electricity are obtained by the Galerkin discrete method. Finally, the nonlinear frequency response equations of the microsheet are derived through the multi-scale method. By using the global residual harmonic balance method, nonlinear vibration characteristic of the MFC-GP microsheet are discussed with respect to nonlocal parameters, volume fraction of graphene, and aspect ratio, which have a significant impact on the dynamic behaviors of the microsheet. The findings will provide a theoretical guidance for engineering design of such microsheets.