Nonlocal plate model for free vibrations of single-layered graphene sheets

Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.