Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments

Nonlinear vibration behavior is presented for a simply supported, rectangular, single layer graphene sheet in thermal environments. The single layer graphene sheet is modeled as a nonlocal orthotropic plate which contains small scale effects. The nonlinear vibration analysis is based on thin plate theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties are assumed to be 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 MD simulation results with the numerical results obtained from the nonlocal plate model. The results show that with properly selected small scale parameters and material properties, the nonlocal plate model can provide a remarkably accurate prediction of the graphene sheet behavior under nonlinear vibration in thermal environments.