Circular Plates Under Hard Excitations to Include Casimir Effect: Amplitude-Voltage Response of Superharmonic Resonance of Second Order

Abstract

Abstract This paper deals with voltage-amplitude response of superharmonic resonance of second order of electrostatically actuated clamped MEMS circular plates. A flexible MEMS circular plate, parallel to a ground plate, and under AC voltage, constitute the structure under consideration. Hard excitations due to voltage large enough and AC frequency near one fourth of the natural frequency of the MEMS plate resonator lead the MEMS plate into superharmonic resonance of second order. These excitations produce resonance away from the primary resonance zone. No DC component is included in the voltage applied. The equation of motion of the MEMS plate is solved using two modes of vibration reduced order model (ROM), that is then solved through a continuation and bifurcation analysis using the software package AUTO 07P. This predicts the voltage-amplitude response of the electrostatically actuated MEMS plate. Also, a numerical integration of the system of differential equations using Matlab is used to produce time responses of the system. A typical MEMS silicon circular plate resonator is used to conduct numerical simulations. For this resonator the quantum dynamics effects such as Casimir effect are considered. Also, the Method of Multiple Scales (MMS) is used in this work. All methods show agreement for dimensionless voltage values less than 6. The amplitude increases with the increase of voltage, except around the dimensionless voltage value of 4, where the resonance shows two saddle-node bifurcations and a peak amplitude significantly larger than the amplitudes before and after the dimensionless voltage of 4. A light softening effect is present. The pull-in dimensionless voltage is found to be around 16. The effects of damping and frequency on the voltage response are reported. As the damping increases, the peak amplitude decreases. while the pull-in voltage is not affected. As the frequency increases, the peak amplitude is shifted to lower values and lower voltage values. However, the pull-in voltage and the behavior for large voltage values are not affected.