ROM of Superharmonic Resonance of Fourth Order of Electrostatically Actuated Clamped MEMS Circular Plates: Voltage Response

Abstract

This paper investigates the voltage-amplitude response of superharmonic resonance of fourth order of electrostatically actuated clamped MEMS circular plates. The system consists of flexible MEMS circular plate parallel to a ground plate. Hard excitations (voltage large enough) and AC voltage of frequency near one eight of the natural frequency of the MEMS plate resonator lead it into a superharmonic resonance. Hard excitations produce actuation forces large enough to produce resonance away from the primary resonance zone. There is no DC component in the voltage applied. The partial differential equation of motion describing the behavior of the system is solved using two modes of vibration reduced order model (ROM). This model is solved through a continuation and bifurcation analysis using the software package AUTO 07P which produces the voltage-amplitude response (bifurcation diagram of the system, and a numerical integration of the system of differential equations using Matlab that produces time responses of the system. Numerical simulations are conducted for a typical MEMS silicon circular plate resonator. For this resonator the quantum dynamics effects such as Casimir effect or Van der Waals effect are negligible. Both methods show agreement for the entire range of voltage values and amplitudes. The response consists of an increase of the amplitude with the increase of voltage, except around the value of 4 of the dimensionless voltage where the resonance shows two saddle-node bifurcations and a peak amplitude about ten times larger than the amplitudes before and after the dimensionless voltage of 4. The softening effect is present. The pull-in voltage is reached at large values of the dimensionless voltage, namely about 14. The effects of damping and frequency on the voltage response are reported. As the damping increases, the peak amplitude decreases for the resonance. However, the pull-in voltage is not affected. As the frequency increases, the resonance zone is shifted to lower voltage values and lower peak amplitudes. However, the pull-in voltage and the behavior for large voltage values are not affected.