Dynamic Analysis of a Double-sided Actuated MEMS Oscillator Using Second-order Averaging

A Bhushan, M Inamdar, D Pawaskar
unpublished
MEMS oscillators have numerous applications as ultra-sensitive sensors, switches, and signal-processing elements. An important class of MEMS oscillators is double-sided electro-statically actuated microbeams. This investigation is concerned with analytical study of nonlinear resonance behaviour of such oscillators using averaging method. We have modelled a microbeam oscillator using Euler-Bernoulli beam theory and Galerkin formulation. The model takes into account the classical nonlinearities
more » ... al nonlinearities of geometric and electrostatic origin along with the effects of both linear and nonlinear damping. The formulated mathematical model is a single-degree of freedom quintic oscillator and contains both symmetric cubic and quintic nonlinearities and asymmetric quadratic and quartic nonlinearities. Second-order averaging method, in contrast to first-order averaging method which is suitable only for symmetric nonlinearities, has been employed to take into account both symmetric and asymmetric nonlinear terms. The averaging solution is validated by comparing the results with numerical solutions. Using our analytical solution, change in qualitative nature (hardening, mixed hardening-softening, and softening) of resonance curves with variation of DC voltage has been explained. Our analytical solution is a useful tool for practicing engineers for fast analysis of resonance curves of MEMS oscillators.
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