Multiscale nonlinear frequency response analysis of single-layered graphene sheet under impulse and harmonic excitation using the atomistic finite element method

The atomistic finite element method (AFEM) is a multiscale technique where a sequential mode is used to transfer information between two length scales to model and simulate nanostructures at the continuum level. This method is used in this paper to investigate the nonlinear frequency response of a single-layered graphene sheet (SLGS) for impulse and harmonic excitation. The multi-body interatomic Tersoff-Brenner (TB) potential is used to represent the energy between two adjacent carbon atoms. Based on the TB potential, the equivalent geometric and elastic properties of carbon-carbon bonds are derived which are consistent with the material constitutive relations. These properties are used further to derive the nonlinear material model (stress-strain curve) of carbon-carbon bonds based on the force-deflection curve using the multi-body interatomic Tersoff-Brenner potential. A square SLGS is considered and its nonlinear vibration characteristics under an impulse and harmonic excitation for bridged, cantilever and clamped boundary conditions are investigated using the derived nonlinear material model (NMM). Before using the proposed nonlinear material model, the derived equivalent geometric and elastic properties of carbon-carbon bond are validated using molecular dynamics simulation results. The geometric (large deformation) and material nonlinearities are included in the nonlinear frequency response analysis. The investigated results of the nonlinear frequency response analysis are compared with those of the linear frequency response analysis, and the effect of the nonlinear behavior of carbon-carbon bonds on the frequency response of SLGS is studied.