Shape Optimization of Electrostatically Driven Microcantilevers using Simulated Annealing to Enhance Static Travel Range

Abstract

The objective of this paper is to present a systematic development of the generic shape optimization of elec- trostatically actuated microcantilever beams for extending their static travel range. Electrostatic actuators are widely used in micro electro mechanical system (MEMS) devices because of low power density and ease of fab- rication. However, their useful travel range is often restricted by a phenomenon known as pull-in instability. The Rayleigh- Ritz energy method is used for computation of pull-in parameters which includes electrostatic potential and fringing Field effect. Appropriate width function and linear thickness functions are employed along the length of the non-prismatic beam to achieve enhanced travel range. Parameters used for varying the thick- ness and width functions are optimized using simulated annealing with pattern search method towards the end to refine the results. Appropriate penalties are imposed on the violation of volume, width, thickness and area constraints. Nine test cases are considered for demonstration of the said optimization method. Our results indicate that around 26% increase in the travel range of a non-prismatic beam can be achieved after optimiza- tion compared to that in a prismatic beam having the same volume. Our results also show an improvement in the pull-in displacement of around 5% compared to that of a variable width constant thickness actuator. We show that simulated annealing is an effective and Flexible method to carry out design optimization of structural elements under electrostatic loading.