Sensors & Transducers (Jun 2013)
Model to Analyze Micro Circular Plate Subjected to Electrostatic Force
Abstract
In this paper a distributed model with three possible static modes was presented to investigate the behavior of the plate subjected to electrostatic force and uniform hydrostatic pressure both before pull in and beyond pull in. The differential governing equation of the micro circular plate specifically used for numerical solution of the three modes, in which the singularity at the center of the micro plate did not occur, was presented based on the classical thin plate theory, Taylor's series expansion and Saint-Venant's principle. The numerical solution to the differential governing equation for the different mode was mainly attributed to solve for one unknown boundary condition and the applied voltage, which could be obtained by using a two-fold method of bisection based on the shooting method. The voltage ranges over which the three modes could exist and the points where transitions occurred between the modes were computed. Incorporating the above numerical solution to the applied voltage at the normal mode with some constrained optimization method, pull-in voltage and the corresponding pull-in position can automatically be obtained. In examples, the entire mechanical behavior of the circular plate over the operational voltage ranges was investigated and the effects of different parameters on pull-in voltage were studied. The obtained results were compared with the existing results and good agreement has been achieved.
