Nonlinear dynamic behavior of single-layer graphene under uniformly distributed loads

An atomistic-continuum multiscale approach is used to simulate the nonlinear dynamic behavior of simply-supported single layer graphene sheets subject to a uniformly distributed out-of-plane load. The dynamic equation of motion is derived and solved by the Newmark-β method. The evolution of surface morphology and the nonlinear effects in terms of geometrical and material nonlinearities can be captured by iteratively updating the system stiffness. It is found that the natural frequencies of simply-supported graphene sheets almost remain constant when the external load is in a small range. The present solutions are in good agreement with those results obtained from the linear vibration analysis by a semi-analytical method. As the applied load increases continuously, this gives rise to an elongation of graphene to increase the natural frequency. Based on the numerical approach, the surface morphology evolution of graphene can be visualized and explored.