弹性边界与边缘场对静电微梁谐振器非线性动力学影响研究

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摘要微加工误差、制造缺陷或创新设计，均可导致微机电系统微梁谐振元件的实际边界偏离理想固支边界，因此研究弹性边界谐振器的静动力学问题成为微机电技术发展的必然。本文综合考虑中性面变形、静电力边缘效应、弹性边界等因素建立了静电驱动微梁谐振器的分布质量模型，应用Galerkin方法研究了弹性边界和边缘场对于系统静态位移与谐振频率的影响，进而以收敛的五阶离散静态解为基础，引入单自由度离散模型，并应用多尺度方法研究了小幅振动情况下弹性边界和边缘场对于系统主共振频响特性的影响。通过将上述分析与高阶Galerkin离散结果对比，可得到以下结论：与理想固支边界对比，弹性边界可导致系统基频下降，临界位移增大，静态吸合电压降低，幅频响应曲线的幅值增大；边缘效应使得静电力增大，对系统产生类似弹性边界的影响。该结果为实现节能谐振器提供了理论基础。

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	常云霞1
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	张琪昌1
	韩建鑫3

关键词 ：静电微梁谐振器, 弹性边界, 边缘效应, 多尺度方法, 伽辽金离散方法, 主共振

Abstract：Deviation of the actual system from the ideal supporting conditions is mainly caused by micromachining errors, manufacturing defects or innovative designs. It is necessary to settle the problem of flexible boundary research. In this paper, we consider the neutral plane tension, fringing field and flexible boundary factors to establish the distribution quality model of electrostatically driven microbeam resonators. The effects of elastic boundary and fringing field on the static displacement and resonant frequency of the system are studied by using the Galerkin method. Based on the convergent fifth-order discrete static solution, a single-DOF discrete model is introduced. The effects of elastic boundary and fringing field on the frequency response characteristics of the main resonance of the system are studied via the method of multiple scales. By comparing the above analysis with high-order Galerkin discrete results, the following conclusions can be drawn. The flexible boundary leads to the displacement and rotation angle of the ends of the micro-beam, furtherly, the resonant frequency is decreased, critical displacement is increased, static pull-in voltage is decreased and the amplitude of the amplitude-frequency curve is increased. The edge effect leads to the increase of electrostatic force and has a similar effect on the system. The results provide a theoretical basis for implementing energy-saving resonators.

Key words： Electrostatic microbeam resonator flexible boundary fringing effect the method of multiple scales Galerkin method primary resonance

收稿日期: 2019-05-13 出版日期: 2020-09-15

引用本文:

常云霞1,2，张琪昌1，韩建鑫3. 弹性边界与边缘场对静电微梁谐振器非线性动力学影响研究[J]. 振动与冲击, 2020, 39(18): 125-131.
CHANG Yunxia1,2，ZHANG Qichang1，HAN Jianxin3. Influence of flexible boundary and fringing field on the nonlinear dynamic performance of electrostatic microbeam resonators. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(18): 125-131.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I18/125

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