We consider an electrostatically actuated torsional micromirror, a key element of recent optical microdevices. The mechanical response is analyzed with specific emphasis on its nonlinear features. We show that the mirror motion is an example of parametric resonance, activated when the drive frequency is twice the natural frequency of the system. The numerical model, solved with a continuation approach, is validated with very good accuracy through an extensive experimental campaign.

We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanical signal processing functions.

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