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.

在本文中，研究了两个频率比约为1：3的非线性耦合微束的内部共振响应，并通过实验观察到了一种有趣的现象，称为频率锁定。建立了耦合系统的非线性动力学模型，并用多尺度方法对其进行求解，并通过解析确定了触发频率锁定的幅度区域。发现振幅区域是可调的，并且深入研究了耦合强度和驱动强度对振幅区域的影响。分析和实验结果表明，较大的耦合强度和驱动强度将导致较大的振幅区域。