Characterizing nonlinear vibration behavior of bilayer graphene thin films

Double layered graphene sheets (DLGSs) have attracted increasing attention due to its unique excellent properties. The present work studies the geometrically nonlinear vibration behavior of DLGSs using von Kármán plate model incorporated with nonlocal elasticity theory accounting for the small scale effect. The element-free kp-Ritz method is then employed to solve the obtained coupled partial differential equations. The effectiveness of the present nonlocal element-free kp-Ritz method is verified through comparison with the published results. The influence of side length, boundary condition, aspect ratio and nonlocal parameter on the geometrically nonlinear vibration behavior of DLGSs are investigated. Ultimately, it is found that the effect of boundary conditions, side length, aspect ratio and nonlocal parameter can approximately be neglected, when compared with that of vdW interaction which exists between adjacent layers of DLGSs.