A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams

A comprehensive model of an electrostatically actuated microcantilever beam separated from the ground plane by relatively larger gap is formulated accounting for the nonlinearities of the system arising out of electric forces, geometry of the deflected beam and the inertial terms. Since the gap is relatively large, the electrostatic model is formulated incorporating higher order correction of electrostatic forces. First static analysis is carried out to match the results obtained from the proposed model with the results provided by other researchers. It is observed that reduced order model exhibits good convergence when five or more number of modes is considered for the analysis. Dynamic analysis of the model is performed with five modes. The study indicates that although electrostatic forces cause softening characteristics whereas geometric nonlinearity produces stiffening effect on the microstructure, the nonlinearities play a significant role when pull-in occurs. The consideration of slope and curvature of deformable electrode for modelling the electrostatic forces for large gap separations predicts more accurate results. For applications in and around pull-in zone, the large deflection model needs to be considered for effective design.