Graphene MEMS resonator: model formulation and computational investigation

Abstract

This study investigates the static and time-dependent response of graphene-based cantilever beam resonators when subjected to electrostatic forces applied at their free ends. A detailed examination of the system’s behavior is carried out, where the nonlinear governing relation is derived through the energy approach in conjunction with Hamilton’s principle. An explicit analytical expression for the nonlinear static case is presented. In addition, the effective stiffness coefficient for a lumped-parameter model of the cantilever beam loaded at its tip is determined, which provides the basis for a thorough exploration of the system’s dynamics. Special emphasis is placed on the onset of dynamic pull-in phenomena under both steady and oscillatory excitations, with analytical forecasts confirmed by numerical computations. The findings indicate that the system maintains periodic oscillations whenever the excitation parameters remain below a critical threshold defined by a separatrix curve. Once the parameters surpass this limit, pull-in instability takes place, leading the beam to collapse onto the substrate. Furthermore, the effect of excitation frequency on the resonator’s behavior under harmonic loading is assessed. Simulation results demonstrate that selecting a frequency close to the natural resonance of the beam may, under specific parameter ranges, induce structural failure.