Highly Accurate Analytical Approximate Solutions of the Electrostatically Actuated Parallel Plates

Abstract

This paper is concerned with highly accurate analytical approximate solutions to dynamic oscillation of the parallel-plates model of an electrostatic micro-actuator. A potential difference is applied between the two electrodes to obtain a desired oscillatory effect, and the top movable electrode is suspended over the bottom fixed electrode by a linear suspension. The periodic oscillation solutions are obtained by generalizing the second-order Newton-harmonic balance (HB) method. The procedure obtains brief and accurate analytical approximate solutions for a large range of oscillation amplitudes with only one iteration step, the analytical approximate solutions show excellent agreement with the “exact” solution yielded by numerical integration. These analytical approximate solutions can be applied to analyze and design micro- and nano-devices employing electrostatic parallel plates.

Keywords

• Parallel plate
• MEMS
• analytical approximation
• second-order Newton iteration
• harmonic balance