梳齿结构与振动梁复合的硅微谐振器的非线性分析

谐振式MEMS传感器的输出信号为频率信号，具有高精度和强抗干扰能力等优点，是微传感器的重要发展方向之一. 但是这类传感器振动具有的非线性会导致振动幅度噪声耦合到频率输出进而对器件的噪声性能产生不利影响，所以对谐振器非线性振动的特性进行分析显得十分重要. 以梳齿结构与振动梁复合的谐振器为研究对象，推导出谐振梁的力-位移方程、振动微分方程，并与实验结果比对，曲线具有很好的吻合度，证明了理论的正确性. 同时表明结构机械非线性主要受谐振梁厚度影响；非线性失稳的临界状态会使结构发生频率跳跃，增加结构阻尼能有效增大系统稳定响应的位移和输出电压信号，同时利用结构非线性失稳后的上跃频率设计器件具有良好的稳定性. 

Nonlinear Analysis of Silicon Microresonator with Vibrating Beam Integrated with Comb Fingers Structure

The output signal of the resonant MEMS sensor is a frequency signal, which has the advantages of high precision and strong anti-interference ability. It is one of the important development directions of micro sensors. However, the non-linearity of the vibration of this type of sensor will cause vibration amplitude noise to be coupled to the frequency output and adversely affect the noise performance of the device. Therefore, it is very important to analyze the nonlinear vibration characteristics of the resonant accelerometer. Taking the resonator with vibrating beam integrated with comb fingers structure as research object, the force-displacement equation and the vibration differential equation of the resonant beam were derived. Compared with the experimental results, the curves are in good agreement, which proves the correctness of the theory. At the same time, the results show that the mechanical nonlinearity of the structure is mainly affected by the thickness of the resonance beam; the critical state of nonlinear instability will cause the structure to jump in frequency. Increasing structural damping can effectively increase the displacement of the stable response of the system and the output voltage signal. In addition, devices designed under the jump-up frequency after structural nonlinear instability have good stability.