An improved method for the mechanical behavior analysis of electrostatically actuated microplates under uniform hydrostatic pressure

Microplates are essential components of the most electrostatically actuated microdevices. Their mechanical behavior is influenced not only by electrostatic force, but by hydrostatic pressure of the environment. This paper presents an improved reduced-order model for an electrostatically actuated microplate under uniform hydrostatic pressure with a novel method for treating the electrostatic force. The model was developed using the Galerkin method and turns the partial-differential equation governing the plate into an ordinary equation system. Using an axisymmetric deflection function and the first-order Taylor series expansion of the electrostatic force, explicit expressions for the deflection and pull-in voltage of the microplate under the electrostatic force alone, and under both electrostatic force and hydrostatic pressure, were derived. The expressions with only the electrostatic force considered can predict the pull-in voltage with a higher accuracy and the deflection within a large range (from the undeformed state to the pull-in position) compared with literature. The expressions for both types of loadings show a better prediction accuracy when the pressure changes in the lower pressure range. The derived expressions are applicable to the electrostatically actuated configurations where the ratio of the plate diameter to its thickness varies from 100 to 40, and the electrode distance is smaller than or equal to the thickness. These theoretical analyses were validated with finite element method simulations and previous literature.