A Generalized Model of Electrically Actuated, Microbeam-Based MEMS Devices

We present a model of electrically actuated microbeam-based MEMS devices incorporating the nonlinearities associated with moderately large displacements and electric forces. The model can handle any capacitor configuration disposing of the complete electrode-overlapping (parallel-plate theory) restriction. The boundary-value problem describing the static deflection of the microbeam under the electrostatic loading is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Results generated by our model for the parallel-plate case are in agreement with published results. Our results show that the underlying assumptions of the closed-form formula of the parallelplate case underestimates the electrostatic force and leads to an overestimation of the pull-in voltage. The model provides an analytical tool to predict the static and dynamic response of any electrically actuated MEMS device based on clamped-clamped microbeams.