The Non-linear Dynamic Response of Microstructures

Abstract

This paper presents the results of the solutions of the non-linear differential equation that models the dynamic performance of a microstructure such as a cantilever beam when is subjected to uniform electrostatic field. This situation is encountered in all capacitive MEMS sensors. The mass-damper-spring model is used to evaluate the critical pull-in voltage yield by the solution of the non-linear differential equation. This model is analyzed based on the adopted models in the literature dealing with the stiffness of the cantilever beam. The one degree of freedom non-linear differential equation used to model the dynamics of the cantilever subjected to electric field set close to pull-in is stiff and the only correct solution is yield by Isode algorithm. The equivalent stiffness of the model was considered based on four different models selected from the open literature. The validity of the solution was confirmed through experimental tests. The stiffness model corresponding to the best match for the deflection model is proved to be different from the one that yields the best match in the resonant frequency.