Full Operational Range Dynamic Modeling of Microcantilever Beams

Microcantilever beams are frequently utilized in microelectromechanical systems. The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer, which has a significant effect on the behavior of the system. Three possible configurations of the beam over the operational voltage range are floating, pinned, and flat configurations. In this paper, a systematic method for deriving dynamic equation of microcantilevers for all configurations is presented. First, a static study is performed on deflection profile of the microcantilever under electrostatic force. After that, 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 are derived. A comparison between modeling results and previous experimental data that has been used for validation of the model shows a good agreement.