耦合组合刚度非线性能量阱的线性振子动力学分析

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摘要将非线性能量阱（NES）连接到线性或弱非线性结构能吸收振动能量以达到减少振动的目的，在被动减振中具有重要的意义。该研究对耦合组合刚度NES的线性振荡器进行了动力学建模和分析，并给出了NES系统参数对减振效果的影响。首先，利用复变量平均法对耦合组合刚度NES的系统进行建模,得到了系统的慢变方程。其次，分析了鞍结分岔和Hopf分岔平衡点个数、稳定性与组合刚度NES系统参数的关系，并给出了激励幅值、频率变化对线性振子幅值的影响，这为后面减振应用的优化提供合理的参数选值具有重要意义。再次，利用能量谱和Poincare映射分析了各部分质量比、激励幅值、NES刚度和阻尼对系统减振的影响，发现了各参数对振动抑制的影响规律。最后利用能量谱验证了组合刚度NES的减振的优越性。
关键词：非线性能量阱；减振；鞍结分岔；Hopf分岔；Poincare映射；能量谱

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	张运法1
	孔宪仁1
	岳程斐2

关键词 ：非线性能量阱, 减振, 鞍结分岔, Hopf分岔, Poincare映射, 能量谱

Abstract：Connecting a nonlinear energy sink (NES) to a linear or weakly nonlinear structure can absorb vibration energy to achieve the purpose of reducing vibration, which is of great significance for passive vibration suppression. In this study, the dynamic modeling and analysis of the linear oscillator with combined stiffness NES are carried out, and the influence of NES system parameters on the vibration mitigation effect is given. Firstly, the complex variable average method is applied to model the system with combined stiffness NES, and the slow variation equation of the system is obtained. Secondly, the relationship between the number of saddle knot bifurcation equilibrium points or the stability of Hopf bifurcation and the parameters of the system with combined stiffness NES is analyzed, and the influence of excitation amplitude and frequency on the amplitude of linear oscillator is given. It is of great significance to provide reasonable value selection suggestions for the optimization of vibration reduction applications in the following sections. Thirdly, the energy spectrum and Poincare mapping are used to analyze the influence of each part's mass ratio, excitation amplitude, NES stiffness and damping on the vibration reduction of the system, and discover the influence rules of each parameter on vibration suppression. Finally, the vibration suppression effect of the proposed NES with combined stiffness is verified by the energy spectrum.
Key words: Nonlinear energy sink; vibration suppression; saddle-node bifurcation; Hopf bifurcation; Poincare mapping; energy spectrum

Key words： Nonlinear energy sink vibration suppression saddle-node bifurcation Hopf bifurcation Poincare mapping energy spectrum

收稿日期: 2021-04-28 出版日期: 2022-07-15

引用本文:

张运法1，孔宪仁1，岳程斐2. 耦合组合刚度非线性能量阱的线性振子动力学分析[J]. 振动与冲击, 2022, 41(13): 103-111.
ZHANG Yunfa1, KONG Xianren1, YUE Chengfei2. Dynamic analysis of linear oscillator with coupled combined stiffness NES. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(13): 103-111.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I13/103

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