Molecular dynamics simulation of vibrational behavior of annular graphene sheet: Identification of nonlocal parameter.

To obtain accurate results from the nonlocal plate theory, the nonlocal parameter should be properly determined. In this paper, practicing a molecular dynamics simulation, the nonlocal plate theory was presented for free vibration analysis of annular graphene sheets. Accuracy and stability of results are validated by published results. Calculations are performed for different boundary conditions and geometrical properties. Results reveal that inner and outer radius induce significant effects on the nonlocal parameter. This nonlocal parameter extracted based on Molecular Dynamics (MD) in the nonlocal theory can determine the natural frequencies of annular graphene sheets, conveniently, whereas the molecular dynamics simulation demands a lot of time.