Synchronization is a well-known phenomenon in nonlinear dynamics that is used to lock the frequencies of two oscillators for frequency stabilization applications. The simplest evidence of such frequency entrainment occurs between a self-sustained oscillator and an external tone2, when the latter is swept around the resonance frequency of the oscillator. Synchronization between two oscillators with frequencies related by an integer ratio can occur but requires coupling between the two modes. We present an experimental study of synchronization between two resonance modes of a single resonator, where the second mode is nearly the third harmonic of the first mode. Due to intrinsic electro-mechanical coupling between the two modes, synchronization will occur for a specific frequency range known as synchronization range. We show by increasing the amplitude of the first mode in the nonlinear Duffing regime, the synchronization range will increase.
Project end date: 01/29/18