Bifurcation behavior for mass detection in nonlinear electrostatically coupled resonators
Bifurcation behavior for mass detection in nonlinear electrostatically coupled resonators
复制标题
非线性静电耦合谐振器中质量检测的分叉行为
DOI：
10.1016/j.ijnonlinmec.2019.103366
复制
发表时间：
2020-03-01
影响因子：
3.2
通讯作者：
Shao, Mingyu
中科院分区：
文献类型：
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作者：
Li, Lei;Zhang, Wenming;Shao, Mingyu
非线性耦合振动广泛存在于耦合共振结构中，可以导致复杂的动力学分岔行为，拓展了基础物理学的研究范围。本文提出了一种利用非线性静电耦合谐振器中的分叉跳跃现象进行微小质量检测的新方法。在考虑基频激励的情况下，利用汉密尔顿原理和伽辽金方法，得到了描述静电耦合谐振传感器的一对一内谐振方程。然后，引入摄动分析方法，研究了系统的小振幅振动响应和稳定性。通过分岔分析，发现非线性静电耦合谐振器中存在孤立响应分支，并给出了产生这种现象的物理条件。典型地，我们演示了利用两个静电耦合微梁谐振器的分叉跳跃现象来实现质量定量检测和阈值检测，克服了非线性振动中频率漂移引起的检测不准确性。最后通过数值实验验证了该方法的有效性。本文的研究结果在微质量检测中具有潜在的应用价值。
The nonlinear coupled vibrations widely exist in coupled resonant structures, which can lead to complex dynamic bifurcation behavior and expand the research scope of fundamental physics. A new micro-mass detection method is proposed by using bifurcation jumping phenomenon in nonlinear electrostatically coupled resonators in this article. Considering the fundamental frequency excitation, the one-to-one internal resonance equations to describe electrostatically coupled resonant sensor are obtained by using Hamilton's principle and Galerkin method. Then, the perturbation analysis method is introduced to study the response and stability of the system for small amplitude vibration. Through bifurcation analysis, it is found that the isolated response branches appear in nonlinear electrostatically coupled resonators and present the physical conditions of this phenomenon. Typically, we demonstrate the exploitation of the bifurcation jump phenomena of two electrostatically coupled microbeam resonators to realize the mass quantitative detection and threshold detection, which overcomes the detection inaccuracy caused by frequency drift in the nonlinear vibration. Finally, the numerical experiments verify the validity of the method. The results of this paper can be potentially useful in micro-mass detection.