Bifurcation Analysis on the Periodic Response of a Comb Drive MEMS Resonator

In this paper, we investigate the bifurcation characteristics of a comb drive MEMS resonator. The method of averaging and the residue theorem are used to get a more accurate analytical solution for the periodic response. Then, the singularity theory is employed to give the transition sets on the DC-AC voltage plane and the lateral separation-quality factor plane, which divide the planes into 9 persist regions. The corresponding bifurcation diagrams are present to discuss the jump phenomena of the periodic response, and the influences of the parameters on the amplitude-frequency response are studied. We also attempt to analyze the feasibility for the resonators working in the nonlinear regions and give the available frequency range and the available maximum amplitude of the nonlinear response. With the increase of the DC voltage, the amplitude-frequency curves change from hardening to softening, and the lateral separation has the opposite effect. The amplitude-frequency curves increase along the backbone curves with the AC voltage and quality factor. The response curves of softening or hardening characteristics have enough available frequency range and large available amplitudes, which may be more appropriate for the operation of the resonator than those of the mixture characteristics.