A Computationally Efficient Model for Analyzing an Electro-Statically Driven MEMS Device Embedded in a Dielectric Fluid

A computationally efficient model is developed for investigating the dynamics of the voltage-driven MEMS device embedded in a dielectric fluid. The lubrication theory is applied to extract the effect of device-medium interaction and MEMS device is modeled as rigid plate by neglecting higher-order plate deformation. As a result, a 2^nd order nonlinear ordinary differential equation is derived that describes the dynamic motions of a suspended plate in a fluid medium under electrostatic voltage loading and squeezed thin film damping that may allow for slip boundary conditions. Solutions are obtained based on the governing equation and characteristic dimensions and materials parameters for a MEMS device. Some interesting results are obtained: two possible static solutions are shown to exist when a combined dimensionless parameter is below a critical threshold value, which is determined from solving a cubic algebraic equation. Two solutions merge into one when the aforementioned parameter reaches a critical value. No static solution exists when the parameter exceeds the critical value - indicating no force balance is possible between the applied driving voltage and the restoring capability of the support flexure. A critical pull-in voltage may be defined accordingly. Dynamic solution is obtained by numerically solving the nonlinear differential equation. Different damping effect is shown to play a crucial role in determining how fast the "equilibrium position" can be reached and how much "ringing" the MEMS plate may be subject to under given loading and damping conditions. Other parameters such as flexure design, operating frequency and pixel plate, etc are also examined with this model