A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping

We present a new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. Our approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the electrostatic forcing of the capacitor airgap, the restoring force of the microplate and the applied in-plane loads. It also accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. Our theoretically calculated quality factors are in excellent agreement with available experimental data and hence our methodology can be used to simulate accurately the dynamics of flexible microstructures and predict their quality factors under a wide range of gas pressures. Because the pressure distribution is related analytically to the deflection, the dimension of the coupled structural-fluidic problem and hence the number of global variables needed to describe the dynamics of the system is reduced considerably. Consequently, the new approach can be significant to the development of computationally efficient CAD tools for microelectromechanical systems.