Dynamic Analysis of electrostatically actuated fixed-fixed microbeams with midplane-stretching effects

We explore the undamped response of step-voltage driven parallel plates and fixed-fixed microbeams. We consider a third order correction in the parallel plate system as a reduced order system to model mid-plane stretching in fixed-fixed beams. In both cases, we employ energy methods to determine the threshold values displacement and voltage. This is the point beyond which there is no oscillatory motion. The dynamic pull-in parameters of the corresponding microactuator model are identified as these critical values. We thoroughly analyze the effects of mid-plane stretching in fixed-fixed microbeams. Additionally, the phase portraits for these actuators are also thoroughly examined. Empirical relations for the oscillation period/switching time for these microactuators are also developed. These results correlate to a high accuracy to previously published results.