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具有柔性支撑的电驱动拱的非线性耦合振动

Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports.

作者信息

Wang Ze, Ren Jianting

机构信息

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710129, Shaanxi Province, China.

出版信息

Micromachines (Basel). 2019 Oct 28;10(11):729. doi: 10.3390/mi10110729.

DOI:10.3390/mi10110729
PMID:31661880
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6915446/
Abstract

The nonlinear coupled vibration of an electrically actuated arch microbeam has attracted wide attention. In this paper, we studied the nonlinear dynamics of an electrically actuated arch microbeam with flexible supports. The two-to-one internal resonance between the first and second modes is considered. The multiple scales method is used to solve the governing equation. Four first-order ordinary differential equation describing the modulation of the amplitudes and phase angles were obtained. The equilibrium solution and its stability are determined. In the case of the primary resonance of the first mode, stable periodic motions and modulated motions are determined. The double-jumping phenomenon may occur. In the case of the primary resonance of the second mode, single-mode and two-mode solutions are possible. Moreover, double-jumping, hysteresis, and saturation phenomena were found. In addition, the approximate analytical results are supported by the numerical results.

摘要

电驱动拱微梁的非线性耦合振动引起了广泛关注。本文研究了具有柔性支撑的电驱动拱微梁的非线性动力学。考虑了第一和第二模态之间的二对一内共振。采用多尺度法求解控制方程。得到了描述振幅和相位角调制的四个一阶常微分方程。确定了平衡解及其稳定性。在第一模态主共振情况下，确定了稳定周期运动和调制运动。可能会出现双跳现象。在第二模态主共振情况下，可能存在单模和双模解。此外，还发现了双跳、滞后和饱和现象。此外，数值结果支持了近似解析结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/2a66588a46e3/micromachines-10-00729-g015.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/d72d0a20c921/micromachines-10-00729-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/77fa7dd8190a/micromachines-10-00729-g011.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/3c14ebc6e025/micromachines-10-00729-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/4484142f7e62/micromachines-10-00729-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/2a66588a46e3/micromachines-10-00729-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/4f8ff6c7cca3/micromachines-10-00729-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/f3699e4d4934/micromachines-10-00729-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/40688394e352/micromachines-10-00729-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/14f9f54b5706/micromachines-10-00729-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/76e486c698d1/micromachines-10-00729-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/6c0eeb4671a7/micromachines-10-00729-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/d271697cc243/micromachines-10-00729-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/6c0783715914/micromachines-10-00729-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/969604f86122/micromachines-10-00729-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/d72d0a20c921/micromachines-10-00729-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/77fa7dd8190a/micromachines-10-00729-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/95f2aa73eb13/micromachines-10-00729-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/3c14ebc6e025/micromachines-10-00729-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/4484142f7e62/micromachines-10-00729-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4c33/6915446/2a66588a46e3/micromachines-10-00729-g015.jpg

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Micromachines (Basel). 2016 Oct 18;7(10):191. doi: 10.3390/mi7100191.
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Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.直接观察非线性微机械振荡器中的相干能量转移。
Nat Commun. 2017 May 26;8:15523. doi: 10.1038/ncomms15523.
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Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters.MEMS 弓形谐振器的模式耦合和非线性共振及其在带通滤波器中的应用。
Sci Rep. 2017 Jan 30;7:41820. doi: 10.1038/srep41820.
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Frequency stabilization in nonlinear micromechanical oscillators.非线性微机械振荡器中的频率稳定化。
Nat Commun. 2012 May 1;3:806. doi: 10.1038/ncomms1813.