Thermal vibrations of single-layered graphene sheets by molecular dynamics.

Dynamics problems in the thermal vibration of single-layered graphene sheets (SLGSs) are investigated using molecular dynamics (MD) method based on the Brenner's second-generation reactive empirical bond order (REBO) potential. The in plane stiffness and Poisson ratio of SLGSs are calculated by stretching SLGSs. The effective thickness of SLGSs is obtained by MD simulations for the thermal vibration of SLGSs through the natural frequency. The natural frequencies for SLGSs of different sizes with initial stress in different temperatures are calculated through MD. The thin plate theory can predict the MD results very well in a certain range of strain. For the nonlinear relation between stress and strain when the strain is very large, the deviation between the MD results and plate theory becomes larger when the strain increases. The difference between the plate theory and the MD results becomes more and more obvious, when the size of graphene sheet is very small.