Hopf Bifurcation in a Disk-shaped Nems

Self-sustained mechanical vibrations of a disc-type microfabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.