Nonlinear Pull-In Study of Electrostatically Actuated MEMS Structures

The pull-in voltage of an electrostatically actuated micro electro mechanical system (MEMS) is determined using the phase portrait analysis of the system. The velocity equation for a simple mass-spring model is derived and the phase portraits are presented. A continuous cantilever system is modelled as a lumped mass-spring system and the method of estimation of its equivalent stiffness, equivalent mass and equivalent areas are explained. The equilibrium positions are obtained from the force balance plot for different voltages and their corresponding conservative energy values are determined. The phase portraits are given for different voltages with their respective energy values from which the pull-in voltage is obtained for this system. This pull-in voltage value is in very close agreement with the previously published results for the same geometric and material parameters