Voltage–amplitude response of alternating current near half natural frequency electrostatically actuated MEMS resonators

Abstract

This paper uses the Reduced Order Model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated MEMS cantilever resonators under soft Alternating Current (AC) voltage of frequency near half natural frequency of the resonator. The voltage is between the resonator and a ground plate, and provides a nonlinear parametric actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as an Euler–Bernoulli cantilever. Two methods of investigations are compared, Method of Multiple Scales (MMS), and Reduced Order Model. Moreover, the instabilities (bifurcation points) are predicted for both cases, when the voltage is swept up, and when the voltage is swept down. Although MMS and ROM are in good agreement for small amplitudes, MMS fails to accurately predict the behavior of the MEMS resonator for greater amplitudes. Only ROM captures the behavior of the system for large amplitudes. ROM convergence shows that five terms model accurately predicts the steady-states of the resonator for both small and large amplitudes.