Vibration and large deformation simulation analysis of graphene membrane for nanomechanical applications

This paper reports an efficient and accurate simulation method for vibrations and deformations of single- and multi-layer graphene membranes. In this method, a graphene membrane is modelled by a 2-D plate element whose thickness is changeable in COMSOL Multiphysics. The graphene is regarded as a linear isotropic elastic material, and the load-deformation behaviour is approximated as a doubly clamped bridge model or a clamped circular membrane. By comparing the simulation results using 2-D plate and another SHELL element with the experiment data respectively, we find that the average errors of 1st-order frequency using 2-D plate and SHELL element for the same membrane are 4% and 43%. Therefore, the simulation method using 2-D plate element is precise and efficient for the nanomechanical analysis of graphene sheets. With the proposed simulation method, the vibrations and nonlinear deformations of the circular and square graphene membranes are analyzed with different dimensions and thicknesses. These simulation results can be the guideline for the nanomechanical device design.