A new approach and model for accurate determination of the dynamic pull-in parameters of microbeams actuated by a step voltage

Accurate determination of pull-in voltage and pull-in position is crucial in the design of electrostatically actuated microbeam-based devices. In the past, there have been many works on analytical modeling of the static pull-in of microbeams. However, unlike the static pull-in of microbeams where the analytical models have been well established, there are few works on analytical modeling of the dynamic pull-in of microbeam actuated by a step voltage. This paper presents two analytical approximate models for calculating the dynamic pull-in voltage and pull-in position of a cantilever beam and a clamped-clamped beam, respectively. The effects of the fringing field are included in the two models. The two models are derived based on the energy balance method. An N-order algebraic equation for the dynamic pull-in position is derived. An approximate solution of the N-order algebraic equation yields the dynamic pull-in position and voltage. The accuracy of the present models is verified by comparing their results with the experimental results and the published models available in the literature.