Closed-form empirical relations to predict the dynamic pull-in parameters of electrostatically actuated tapered microcantilevers

Abstract

We develop novel closed-form empirical relations to estimate the dynamic pull-in parameters of electrostatically actuated linearly tapered microcantilever beams driven by a step-function voltage. A computationally efficient single degree-of-freedom model is employed in the setting of an energy-based technique to characterize the dynamic pull-in of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The model exploits the fundamental mode shape of the respective nonprismatic geometry obtained using the differential transform technique. A unique surface fitting model is proposed to characterize the variations of both pull-in displacement and pull-in voltage over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. The empirical estimates of dynamic pull-in parameters are validated against 3D finite element simulations and available data in the literature. Excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the preliminary design of tapered microcantilever beams.