Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

Abstract

In this paper, nonlinear dynamics and chaos of electrostatically actuated MEMS resonators under two-frequency parametric and external excitations are investigated analytically and numerically. A nonlinear mass-spring-damping model is used to accounting for squeeze film damping and the parallel plate electrostatic force. The micro-structure is excited by a dc bias electrostatic force and a harmonic force with a frequency tuned closely to their fundamental natural frequencies (combination oscillation). The quality factor is calculated for the microcantilever beam of the resonator considering squeeze film damping. The effect of nonlinear squeeze film damping on the frequency response, quality factor, resonant frequency and nonlinear dynamic characteristics of the dynamic system are provided with numerical simulations using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait. The results show that the dynamic system goes through a complex nonlinear vibration as the system parameters change. It is indicated that the effect of nonlinear squeeze film damping should be considered due to its decreasing the quality factor and changing the nonlinear phenomena of the MEMS resonators.