考虑边缘效应的MEMS梳齿谐振器的静动力学特性分析

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摘要 MEMS梳齿谐振器是一种高精度微机械电子元件，广泛应用在航天航空、精密测量、国防军事、通讯等领域，其静动力学问题受到研究人员的广泛关注。静电激励力是研究MEMS动力学的基础，但由于梳齿高纵深比的结构特性，其静电力存在很强的边缘效应现象。本文采用最小二乘法拟合了在边缘效应基础上梳齿结构静电力的模型，分析了边缘效应对MEMS梳齿谐振器动力学行为的影响。探讨了梳齿微谐振器的横向稳定性、谐振频率、软硬特性的区分标准以及线性过渡现象的参数表达式。结果表明：边缘效应模型导致系统稳定区间减小，经典模型高估了微梳齿谐振器的振动稳定性；边缘效应会导致系统固有频率的减小，软化行为增强，线性过渡电压减小；随着梳齿初始间距的增大，系统的线性过渡下的最优设计电压逐渐变大，对应谐振频率逐渐减小。

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关键词 ：梳齿, 边缘效应, 最小二乘拟合, 稳定性

Abstract：Micro-electro-mechanical systems (MEMS) comb resonator is a micro mechanical & electronic component with high precision and widely applied in aerospace, precision measurement, national defense and military, communications and other fields. Its static and dynamic characteristics receive more and more attentions. Due to the particularity of comb structure, the fringe effect of its electrostatic force is very strong. Here, a MEMS comb resonator’s electrostatic force model considering the fringe effect was fitted with the least-squares method. The influence of fringe effect on the dynamic characteristics of a MEMS comb resonator was analyzed. The system’s lateral stability and resonance frequency were explored. The criterion to distinguish the hard character from the soft one was defined. Moreover, two explicit formulas to describe the optimal DC voltage and the equivalent natural frequency when a linear-like state appeared were deduced, respectively. The results showed that the model with the fringe effect causes a smaller stable region of the system compared to the traditional model, the latter over-estimates the stability of a MEMS comb resonator; the fringe effect also causes decrease in the system natural frequency and the transient voltage from hard character to soft one, and enhancement of softening behavior; with increase in the initial spacing of the comb, the designed optimal system voltage increases gradually, while the corresponding resonance frequency decreases.

Key words： comb fringe effect least-squares fitting stability

收稿日期: 2016-12-12 出版日期: 2018-06-28

引用本文:

马贺冲 1，张琪昌 1,陈涛 2，李磊 1. 考虑边缘效应的MEMS梳齿谐振器的静动力学特性分析[J]. 振动与冲击, 2018, 37(13): 71-77.
ZHANG Qi-chang 1 MA He-chong 1 CHEN Tao 2 LI Lei 1. Static and dynamic characteristics of MEMS comb resonators considering fringe effect. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(13): 71-77.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I13/71

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