Shape optimization and dynamic characterization of multiple-electrostatically deformable microbridges

Abstract

The nonlinear nature of electrostatic fields in micromachined structures, such as, cantilevers, bridges or plates, makes it difficult to achieve desired deflection shapes. An analytical approach to predict the static deflection and dynamic behavior of a microbridge subjected to electrostatic fields of multiple electrostatic actuators is presented in this paper. The boundary support conditions of the micromachined structures are nonhomogeneous in nature and are modeled with artificial translational and rotational springs. The static and dynamic behaviors of the microbridge are investigated by the Rayleigh–Ritz method using boundary characteristic orthogonal polynomials. The deflection of the microbridge and the natural frequencies under certain applied voltages are also presented. Least-squares fitting method is used to optimize the applied voltage of actuators in order to generate the desired static deflection. The proposed method is simple and can be easily extended to complicated configurations which are suitable for adaptive optics applications.