Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias

Figure 3

Continuous transition of the frequency response from Hopf bifurcation to cyclic fold bifurcation due to DC bias 𝛿_0𝐷. AC frequency is near natural frequency. (a) Amplitude-frequency response, (b) phase-frequency response, (c) Zone D detail, and (d) Zone E detail. MMS is used. Four cases are shown in all figures: (i) zero DC bias (black lines): 𝛿_0𝐷=0.0, (ii) dark grey lines: 𝛿_0𝐷=0.00002, (iii) grey lines: 𝛿_0𝐷=0.00005, and (iv) light grey lines: 𝛿_0𝐷=0.0001. The AC voltage, fringe, and damping are 𝛿_0𝐴=0.1, 𝑓=0.26, and 𝑐=0.01, respectively.

(a)

(b)

(c)

(d)