Perturbation analysis of entrainment in a micromechanical limit cycle oscillator

We study the dynamics of a thermo-mechanical model for a forced disc shaped, micromechanical limit cycle oscillator. The forcing can be accomplished either parametrically, by modulating the laser beam incident on the oscillator, or non-parametrically, using inertial driving. The system exhibits both 2:1 and 1:1 resonances, as well as quasiperiodic motions and hysteresis. A perturbation method is used to derive slow flow equations, which are then studied using the software packages AUTO and pplane7. Results show that the model agrees well with experiments. Details of the slow flow behavior explain how and where transitions into and out of entrainment occur.