A study of the scale effects on the flexural vibration of graphene sheets using REBO potential based atomistic structural and nonlocal couple stress thin plate models

The flexural vibration of nano-meter sized single layer graphene sheets is studied using a REBO potential based atomistic structural model for a wide range of graphene sheets sizes and chiralities, and with consideration for different boundary conditions, as well as the effects of in-plane forces and environmental stiffness. The scale effects on the vibration of graphene sheets are examined and discussed. A novel nonlocal couple stress thin plate model is then proposed for single layer graphene sheet and is iteratively fitted to the earlier obtained atomistic results to obtain estimations of the scale effect parameters. In addition to the nonlocal parameter, the equivalent Poissonʹs ratio of the plate model of graphene sheet in flexure is also shown to be a scale effect parameter having mostly negative values. This phenomenon is discussed to corroborate the use of couple stress theory in developing the current thin plate model for graphene sheets.