Synchronization of a micromechanical oscillator in different regimes of electromechanical nonlinearity

摘要

In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes of electromechanical nonlinearity to an external tone generated by a secondary oscillator. The micromechanical oscillator exhibits a combination of mechanical and electrostatic nonlinearities that were tuned using a bias voltage to adjust the relative importance of third-order and fifth-order stiffness nonlinearities. While it is well-known that third-order stiffness (Duffing) nonlinearity results in a synchronization range that increases with an oscillator's amplitude, little is known about the impact of other nonlinearities. We show that when using Duffing nonlinearity cancellation, higher order nonlinearities dominate, the synchronization range is smaller but has a greater rate-of-increase with oscillation amplitude. When both mechanical stiffness-hardening and electrostatic stiffness-softening nonlinearities are present, the frequency response follows an "s-curve" and, unlike the other conditions, the synchronization range does not increase monotonically with amplitude but instead reaches a minimum when both nonlinearities have similar magnitude. We develop a nonlinear resonator model and show that this model achieves good quantitative prediction of the measured synchronization range in all nonlinear operating regimes studied.