The Stability and Non-linear Vibration Analysis of a Circular Clamped Microplate under Electrostatic Actuation

Abstract

A study was made of the dynamic response of a circular clamped micro-plate actuated by a DC/AC voltage. The analysis considers not only the non-linear electrostatic coupling force, residual stress effect, and hydrostatic pressure acting on the upper surface, but also the squeeze-film damping effect generated by the air gap between the vibrating micro-plate and the fixed substrate. The non-linear governing equation of motion of the circular micro-plate was solved using a hybrid numerical method comprising the differential transformation and the finite difference. It was shown that the numerical results obtained for the pure DC pull-in voltage deviate by no more than 1.6% from the results presented in the literature. The effects of the actuating voltage, hydrostatic pressure, squeeze-film damping, and residual stress on the dynamic response of the clamped circular micro-plate were systematically examined. In addition, the stability of the vibrating micro-plate was investigated examined by reference to phase portraits.