Amplitude region for triggering frequency locking in internal resonance response of two nonlinearly coupled micro-resonators

In this paper, the internal resonance response of two nonlinearly coupled micro beams with frequency ratio approximately 1:3 is investigated and an interesting phenomenon called frequency locking is observed experimentally. A nonlinear dynamic model of the coupled system is established and solved using multi scale method to explain this phenomenon, and the amplitude region for triggering frequency locking is determined analytically. The amplitude region is found tunable and the effects of coupling strength and driving strength on the amplitude region are investigated deeply. The analytical and experimental results show that the greater coupling strength and driving strength will lead to larger amplitude region.