Frequency spectrum of nonlinear oscillations and resonance phenomena for graphene plates

Abstract

The paper studies oscillations of graphene plates under the hypothesis that deformations are much more than the thickness of plate. In this most realistic case the oscillations are described by the system of nonlinear partial differential equations (the Foppl-von Karman equations). This system is reduced to one nonlinear ordinary differential equation and investigated by means of the Bogoliubov-Mitropolsky asymptotic methods. As a result, we have the real frequency spectrum for rectangular graphene plates. Next we have examined the nonlinear resonance effects under forced oscillations. These outcomes can apply for variable strain-induced pseudomagnetic fields. Such fields permit better to understand the properties of flexural phonons connected with transport process. Resonance phenomena play a leading role in application of graphene plates in engineering constructions.