A Very Simple Closed-Form Expression for Pull-In Voltage and Fundamental Frequency of Fixed-Fixed Beam

In this paper, a very simple closed-form expression for pull-in voltage and fundamental frequency of a fixed-fixed beam is presented with appropriate accuracy. We propose a model incorporating all know factors including effects of partial electrode configuration, axial stress, nonlinear stiffening, charge redistribution, and the fringing field effects. For the first time we express an analytic formulation for the pull-in deflection as a function of beam specification. We make an extensive comparison between the results of pull-in voltage obtained by our new expression and well-known approaches proposed in the literature. To do this, we calculate pull-in voltage with our expression for a wide range of beam specification and compare it with numerical, experimental and also other reported expressions. The pull-in voltage model has an average error of %1.29 in comparison to the experimental data for beams with a complete electrode, and %3.37 as compared to the 3D-coupled FEM simulation results for beams with partial electrode. Moreover, we show that the calculated fundamental frequency using proposed model is in good agreement with the experimental result from zero to near the pull-in voltages.