Subharmonic Resonance of One Fourth Order of Electrostatically Actuated MEMS Circular Plates: Amplitude-Frequency Response

This work deals with the amplitude-frequency response subharmonic resonance of 1/4 order of electrostatically actuated circular plates. The method of multiple scales is used to model the hard excitations and to predict the response. This work predicts that the steady state solutions are zero amplitude solutions, and non-zero amplitude solutions which consist of stable and unstable branches. The effects of parameters such as voltage and damping on the response are predicted. As the voltage increases, the non-zero amplitude solutions are shifted to lower frequencies. As the damping increases, the non-zero steady-state amplitudes are shifted to higher amplitudes, so larger initial amplitudes for the MEMS plate to reach non-zero steady-state amplitudes.