Nonlinear dynamic responses of triple-layered graphene sheets under moving particles and an external magnetic field

Abstract

This paper reports the result of an investigation into the nonlinear dynamic responses of triple-layered graphene sheets subjected to moving particles (gas molecules, lithium ion, catalyst molecules, electron, etc.) and an external magnetic field. Based on Von Kármán nonlinear geometric relations and nonlocal elasticity theory, the nonlinear dynamic nonlocal governing equations are found by utilizing the Hamilton's principles and Galerkin method, where Van der Waals forces between two layers of triple-layered graphene sheets are considered. A reformulated differential quadrature method (DQM) is demonstrated to solve the nonlinear dynamic nonlocal governing equations. Effects of some key factors on the nonlinear dynamic characteristics of triple-layered graphene sheets are calculated and described in examples. Results show that the deflection response magnitude for the nonlinear solution is smaller than that for linear, the small scale effect could induce the decline of natural frequencies, the dynamic response is significantly affected by particles moving speed, to increase magnetic field strength could induce the decrease of the dynamic deflection and the increase of resonant frequency at the same time. The presented meaningful results could serve as useful references in the application and design of lithium batteries, nano sensors, and other micro or nano-devices based on laminated graphene sheets.