考虑边缘效应的静电驱动MEMS振子非线性振动定性研究

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (1) : 10-19.

振动理论与交叉研究

考虑边缘效应的静电驱动MEMS振子非线性振动定性研究

李佰洲1，韩建鑫*1,2 ，黄仪1，崔良玉1,2

作者信息 +

Qualitative study on nonlinear vibration of electrostatically actuated MEMS oscillator considering fringing effects

LI Baizhou1, HAN Jianxin*1,2, HUANG Yi1, CUI Liangyu1,2

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摘要

应用非线性动力学理论定性研究了考虑边缘效应的静电驱动微机电系统（micro-electromechanical system，MEMS）振子的非线性主共振问题。首先，应用微分求积法的空间离散处理得到了系统的单自由度动力学方程；其次，应用分岔理论研究了系统的静态分岔特征，推导并定义了无量纲临界立方刚度、一次吸合电压和二次吸合电压；然后，应用多尺度方法得到了系统的频响函数，定义了小幅振动频响软硬特性转换的无量纲临界电压；最后，结合动态吸合条件与软硬转换临界控制方程，讨论了系统的主共振以及阱间跳跃的动态规律。该研究对于定性掌握静电驱动MEMS振子的静动态吸合及主共振响应规律具有理论及工程参考价值。

Abstract

Here, the nonlinear principal resonance problem of an electrostatically actuated micro-electromechanical system (MEMS)
oscillator considering fringing effects was qualitatively studied using nonlinear dynamics theory. Firstly, the spatial discretization with differential quadrature method was adopted to obtain the system’s single degree of freedom dynamic equation. Secondly, static bifurcation characteristics of the system were studied using bifurcation theory, and dimensionless critical cubic stiffness, primary pull-in voltage and secondary pull-in voltage were derived and defined. Thirdly, the multi-scale method was used to obtain the frequency response function of the system, and the dimensionless critical voltage for converting soft-hard characteristics of small amplitude vibration frequency response was defined. Finally, by combining dynamic pull-in conditions with the critical control equation for soft-hard conversion, dynamic laws of the system’s main resonance and inter-trap jumps were discussed. It was shown that this study has theoretical and engineering reference value for qualitatively grasping static and dynamic pull-in and main resonance response laws of electrostatically actuated MEMS oscillators.

导出引用

李佰洲1, 韩建鑫1, 2, 黄仪1, 崔良玉1, 2. 考虑边缘效应的静电驱动MEMS振子非线性振动定性研究[J]. 振动与冲击, 2025, 44(1): 10-19

LI Baizhou1, HAN Jianxin1, 2, HUANG Yi1, CUI Liangyu1, 2. Qualitative study on nonlinear vibration of electrostatically actuated MEMS oscillator considering fringing effects[J]. Journal of Vibration and Shock, 2025, 44(1): 10-19

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