Li Yan, Song Linke, Liang Shuai, Xiao Yifeng, Yang Fuling
School of Mechanical Electronic & Information Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China.
Sensors (Basel). 2020 Dec 16;20(24):7207. doi: 10.3390/s20247207.
This paper aims to develop a resonant accelerometer for high-sensitivity detection and to investigate the nonlinear vibration of the MEMS resonant accelerometer driven by electrostatic comb fingers. First, a nonlinear vibration model of the resonator with comb fingers in a MEMS resonant accelerometer is established. Then, the nonlinear and nonlinear stiffness coefficients are calculated and analyzed with the Galérkin principle. The linear natural frequency, tracking error, and nonlinear frequency offset are obtained by multi-scale method. Finally, to further analyze the nonlinear vibration, a sample-based stochastic model is established, and the uncertainty analysis method is applied. It is concluded from the results that nonlinear vibration can be reduced by reducing the resonant beam length and increasing the resonant beam width and thickness. In addition, the resonant beam length and thickness have more significant effects, while the resonant beam width and the single concentrated mass of comb fingers have little effect, which are verified by experiments. The results of this research have proved that uncertainty analysis is an effective approach in nonlinear vibration analysis and instructional in practical resonant accelerometer design.
本文旨在开发一种用于高灵敏度检测的谐振式加速度计，并研究由静电梳齿驱动的微机电系统（MEMS）谐振式加速度计的非线性振动。首先，建立了MEMS谐振式加速度计中带有梳齿的谐振器的非线性振动模型。然后，利用伽辽金原理计算并分析了非线性刚度系数。通过多尺度方法获得了线性固有频率、跟踪误差和非线性频率偏移。最后，为了进一步分析非线性振动，建立了基于样本的随机模型，并应用了不确定性分析方法。结果表明，通过减小谐振梁长度、增加谐振梁宽度和厚度可以降低非线性振动。此外，谐振梁长度和厚度的影响更为显著，而谐振梁宽度和梳齿的单个集中质量的影响较小，这通过实验得到了验证。本研究结果证明，不确定性分析是非线性振动分析中的一种有效方法，对实际谐振式加速度计的设计具有指导意义。
