Nonlinear subharmonic oscillation of orthotropic graphene-matrix composite

We investigate the nonlinear responses of graphene-matrix composite to harmonic and subharmonic resonances. Assuming anisotropic mechanical properties of graphene, we derive size-dependent governing equations of motion for graphene resting on a matrix based on the von Karman hypotheses and nonlocal elasticity theory. Response of graphene oscillation under a uniform pressure is obtained using the averaging method. We study the effects of length scale as well as the presence of the elastic matrix on harmonic and subharmonic oscillations of graphene. Our results reveal that subharmonic oscillation of order 1/3 can occur when the ratio of excitation to natural frequencies exceeds three. Also, the subharmonic oscillation of the system is triggered in an appropriate initial condition. (C) 2014 Elsevier B.V. All rights reserved.