Amplitude–frequency response of parametric resonance of electrostatically actuated MEMS clamped circular plate

Abstract

This paper investigates the amplitude–frequency response of parametric resonance of a clamped elastic circular plate microelectromechanical system (MEMS) resonator above a parallel ground plate and under electrostatic actuation. Soft AC voltage with frequency near the first natural frequency of the plate is used. This results into parametric resonance. The system is assumed to be weakly nonlinear. Numerical and analytical methods are used to solve the reduced order models of the electrostatically actuated MEMS circular plate resonators in order to obtain the amplitude–frequency response of their parametric resonance. Seven Reduced Order Models (ROM) with one to seven modes of vibration (terms) have been developed and used in this investigation. ROM with one mode of vibration was solved using the Method of Multiple Scales (MMS) and predicted the existence of the resonance. ROMs with two to seven modes of vibration were solved using continuation and bifurcation software AUTO 07p to simulate and predict the amplitude–frequency response. These simulations showed that increasing the number of modes of vibration in the ROM produced better results. However, there is no significant difference between six and seven modes of vibration ROMs. Therefore, the ROM using seven modes of vibration was used in this research. This ROM was also numerically integrated to predict time responses of the MEMS plate. All methods showed an excellent agreement for amplitudes less than 0.5 of the gap. Only ROM using seven modes of vibrations had accurate predictions for all amplitudes, i.e. amplitudes between zero and the gap distance. The frequency response consists of two bifurcations, subcritical and supercritical. The effects of AC voltage and damping on the amplitude–frequency response are reported. Increasing the AC voltage results in shifting of the bifurcations to lower frequencies, subcritical significantly more than supercritical. Increasing the damping results in a narrower frequency range between the bifurcations.