Superharmonic Resonance of Third Order of Electrostatically Actuated MEMS Circular Plates: Effect of AC Frequency on Voltage Response

This paper uses the Reduced Order Model (ROM) as well as the Method of Multiple Scales (MMS) in order to investigate behavior of electrostatically actuated micro-electro-mechanical systems (MEMS) circular plates under superharmonic resonance of third order. ROM is solved using two methods, the first is a continuation and bifurcation approach by using software package called AUTO 07p in order to obtain the voltage response, and the second approach is a numerical integration using the Matlab built in function ode15s for obtaining time responses of the system. Overall MMS and ROM provide similar results, especially in the lower amplitudes. These methods seem to differ at higher amplitudes. The ROM shows a second unstable branch that MMS does not have. The time responses agree with the ROM voltage response. Furthermore, the influences of different parameters such as that of the detuning parameter, and damping are investigated.