Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity

Nonlinear transverse vibration response is investigated for bilayer graphene sheets (BLGSs) in thermal environments by using molecular dynamics simulation and nonlocal elasticity. The BLGS is modeled as a nonlocal double-layered plate which contains small scale effect and van der Waals interaction forces. The geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size-dependent and temperature-dependent, and are obtained from molecular dynamics simulations. The small scale parameter e0a is estimated by matching the natural frequencies of graphene sheets observed from the molecular dynamics simulation results with the numerical results obtained from the nonlocal plate model. The results show that the stacking sequence has a small effect, while the aspect ratio has a moderate effect on the nonlinear vibration response of BLGSs. In contrast, the temperature change has a significant effect on the nonlinear vibration response of BLGSs. The results reveal that the small scale effect also plays an important role in the nonlinear vibration of BLGSs.