A Closed Form Solution for the Pull-in Voltage of the Micro Bridge with Initial Stress subjected to Electrostatic Loads

Abstract

This paper derives a closed form solution with fringing filed effects for the pull-in voltages of the micro fixed-fixed beam subjected to electrostatic loads and initial stress. The closed form solution is derived based on the Euler's beam theory and the energy method. The accuracy of the present closed form solution is verified through comparing with the experimentally measured data conducted in the published works. The error of the present closed form solution is within 1% compared to the experimentally measured data. The present closed form solution is more accurate than the past works and is very simple and highly accurate for implementation in the design and mechanical characterization of the micro devices.