Does vibration amplitude influence the evaluation of nonlocal small scale parameter of single layered graphene sheets?

This study aims to evaluate the nonlocal small scale parameter for large amplitude vibration of single layered graphene sheets (SLGSs) comparing nonlinear resonant frequencies obtained via nonlocal continuum and molecular dynamics (MD) simulations. Nonlinear governing equations of motion are numerically solved employing the pseudo-spectral method to obtain the frequency response. Results reveal that the calibrated small scale parameter decreases when the vibration amplitude increases. Also, from MD simulations it is seen that for all length sizes after an ultimate vibration amplitude around 31% length size, the graphene sheets start to fracture.