The nonlinear mechanical response of an electrostatically actuated doubly-clamped micro-actuator assuming a non-contact based actuation arrangement is examined. The electrostatic actuating force is numerically approximated through solving a nonlinear electrical field problem using a finite-elements based analysis. An electro-mechanical model is established within the framework of the Euler–Bernoulli continuous nonlinear beam theory, where both the nonlinear geometric mid-plane stretching and the nonlinear electric forcing effects have been both taken into consideration. Then, assuming a Galerkin’s based modal expansion technique, the structural behavior of the micro-actuator under the effect of the resultant electric out-of-plane fields is solved numerically. The resultant nonlinear reduced-order model equations are examined to get the deflection of the microbeam against an assumed bias voltage for different vertical initial gap sizes. The snap-through and pull-out voltages of the micro-system are calculated for different assumed initial vertical gap separation. Frequency diagrams are analyzed against any applied DC bias voltage through solving a linearized eigenvalue problem. Thorough parametric simulations indicate a prospect of such bi-stable design of the micro-actuator with large stroke and high fundamental frequency enabling it to be potentially useful for MEMS based high frequency energy harvester devices with bi-stable capabilities.
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