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.
Highlights
Recent technological advances have enabled the fabrication of resonators down to micro- and even nano- scales
We have presented analytical and numerical study of the effect of squeeze film damping on the dynamic responses and nonlinear dynamics of the electrostatically actuated MEMS cantilever resonators under combination resonant condition
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 using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait
Summary
Recent technological advances have enabled the fabrication of resonators down to micro- and even nano- scales. Gallacher et al [12] studied the application of combined external forcing and parametric excitation to the micro-ring gyroscope in order to enable parametric amplification of the dynamic gain of the primary mode by at least two orders of magnitude. Hu et al [15] discussed the resonances of electrostatically actuated micro-cantilevers, while Baskaran and Turner [16] demonstrated the coupled modes parametric resonance. It should be noted, that an important feature of parametric excitation is the ability of stabilizing a statically unstable system.
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