Entrainment of NEMS limit cycle oscillations

MEMS and NEMS resonators have been shown to undergo self- or limit-cycle oscillations when the motion of the device is fedback as a driving force. This can occur, for example, when the device vibrates inside of a laser interference field. The modulation of heating and hence of thermo-elastic stress fields that occurs as the device vibrates in and out of the high intensity regions of the interference field can provide either positive or negative feedback. It has also been shown that the limit cycle oscillations can be entrained, or synchronized, to a low amplitude pilot signal if that signal is close enough to the limit cycle frequency. Examples of pilot signals are inertial drive and modulation of the laser intensity. Once entrained, the frequency can be adjusted within a range of approximately 4% of the resonant frequency. A coupled thermo-mechanical model is developed to explain this behavior. Parameters of the system are calibrated through a combination of experiments and computational simulations. The model is shown to predict limit cycle oscillations, entrainment and hysteresis of entrainment. Parameters of the model are varied and the predictions compared to experiments in order to understand the importance of the various effects considered by the model.