Influence of out-of-plane defects on vibration analysis of graphene: Molecular Dynamics and Non-local Elasticity approaches

Out-of-plane defects may exist in graphene inevitably or purposely. The present study aims at investigating the influence of out-of-plane defects on vibrational analysis of single layered graphene sheets (SLGSs) implementing both nonlocal elasticity and molecular dynamics (MD) simulations. In nonlocal elasticity analysis, the defect is considered as an initial curvature which is modeled by an analytical function having controllable parameters for the amplitude, extension, and location. In molecular dynamics analysis, defects are simulated by inserting inverse Stone-Wales defects in the perfect structure of SLGSs. Both nonlocal continuum and MD simulation results reveal that the defects increase the vibrational frequency. It is shown that classical elasticity overestimates frequencies with a considerable error while the nonlocal plate model can fit MD results by implementing a proper small scale parameter.