Effects of the van der Waals force,squeeze-film damping,and contact bounce on the dynamics of electrostatic microcantilevers before and after pull-in

The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton’s principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling results and previous experimental data that have been used for validation of the model shows a good agreement.