周期激励下接地双稳态非线性能量阱的动力学

中国民航大学学报 ›› 2023, Vol. 41 ›› Issue (4): 51-57.

周期激励下接地双稳态非线性能量阱的动力学

李双宝^a，周新星^b

（中国民航大学 a. 科技创新研究院；b. 理学院，天津 300300）

收稿日期:2022-01-05 修回日期:2022-02-16 出版日期:2023-08-25 发布日期:2023-10-25
基金资助:
国家自然科学基金项目（12172376）

Dynamics of a grounded bistable nonlinear energy sink under periodic excitations

LI Shuangbao^a , ZHOU Xinxing ^b

(a. Science and Technology Innovation Division; b. College of Science, CAUC, Tianjin 300300, China)

Received:2022-01-05 Revised:2022-02-16 Online:2023-08-25 Published:2023-10-25

摘要/Abstract

摘要： 非线性能量阱（NES，nonlinearenergysink）作为一种轻质高效的被动减振装置可有效抑制工程结构的有害振动，对其动力学开展研究对于设计和优化减振装置具有重要的意义。本文探讨了一种接地双稳态非线性能量阱耦合主线性结构的系统在周期激励下的响应过程，分析这类减振装置的优点，并提出设计准则。应用复化平均和多尺度展开方法对耦合系统进行动力学分析，计算出耦合系统的慢不变流形（SIM，slowinvari鄄antmanifold）和外激励阈值，利用Melnikov方法得到了耦合系统的混沌阈值并给出参数优化方案。与线性和立方刚度的减振装置对比展示了该接地双稳态非线性能量阱的优势。

关键词: 接地双稳态动力学, 非线性能量阱, 慢不变流形, Melnikov 方法

Abstract: As a lightweight and efficient passive vibration absorber, nonlinear energy sink (NES) can effectively suppress the harmful vibration of engineering structures, thus the study of the dynamics is significant for the design and opti鄄 mization of the vibration absorber. Under the periodic excitations, the response process of a coupled system of grounded bistable NES and main linear structure is studied to analyze the advantages of this kind of vibration ab鄄 sorber and propose design criteria. The complex averaging and multi-scale expansion methods are applied to an鄄 alyze the dynamics of the coupled system and the slow invariant manifold (SIM) and external excitation threshold of the coupled system are calculated. The chaotic threshold and the parameter optimization scheme of the coupled system are obtained based on the Melnikov method. Furthermore, the comparisons with the vibration absorbers of linear and cubic stiffness demonstrate the advantages of this grounded bistable NES

Key words: grounded bistable dynamics, nonlinear energy sink, slow invariant manifold, Melnikov method

中图分类号:

O322

李双宝, 周新星. 周期激励下接地双稳态非线性能量阱的动力学[J]. 中国民航大学学报, 2023, 41(4): 51-57.

LI Shuangbao , ZHOU Xinxing . Dynamics of a grounded bistable nonlinear energy sink under periodic excitations[J]. Journal of Civil Aviation University of China, 2023, 41(4): 51-57.

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