Mechanical behavior analysis on electrostatically actuated rectangular microplates

Microplates are widely used in various MEMS devices based on electrostatic actuation such as MEMS switches, micro pumps and capacitive micromachined ultrasonic transducers (CMUTs). Accurate predictions for the mechanical behavior of the microplate under electrostatic force are important not only for the design and optimization of these electrostatic devices but also for their operation. This paper presents a novel reduced-order model for electrostatically actuated rectangular and square microplates with a new method to treat the nonlinear electrostatic force. The model was developed using Galerkin method which turned the partial-differential equation governing the microplates into an ordinary equation system. Using this model and cosine-like deflection functions, explicit expressions were established for the deflection and pull-in voltage of the rectangular and square microplates. The theoretical results were well validated with the finite element method simulations and experimental data of literature. The expressions for the deflection analysis are able to predict the deflection up to the pull-in position with an error less than 5.0%. The expressions for the pull-in voltage analysis can determine the pull-in voltages with errors less than 1.0%. Additionally, the method to calculate the capacitance variation of the electrostatically actuated microplates was proposed. These theoretical analyses are helpful for design and optimization of electrostatically actuated microdevices.