Nonlinear Vibration of the Flexoelectric Nanoplate with Surface Elastic Electrodes Under Active Electric Loading

Abstract

This paper mainly studies the effects of surface elastic electrodes and electric loading on the nonlinear vibration of flexoelectric nanoplate. The governing equations are derived based on the von Karman type strain–displacement relations and the flexoelectricity theory. The nonlinear vibration equation is solved by an approximate method. Numerical results reveal that the surface elastic electrodes and the length–width ratio of flexoelectric nanoplate have a more significant effect on the nonlinear resonant frequency of simply-supported nanoplate than that of the all-edge-clamped nanoplate. Meanwhile, the effect of the graphene electrode on the nonlinear resonant frequency is more notable than that of the Al electrode. Additionally, the applied electric loading can significantly affect the nonlinear resonant frequency of the flexoelectric nanoplate. For the nanoplates with different boundary conditions, the applied electric loading has different effects on the nonlinear resonant frequency. This study has certain research significance in the structure design and examination of the flexoelectric nanoplate with electrodes.