一种含放大机构、惯容和接地刚度的动力吸振器的参数优化

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (21) : 308-215.

论文

杨晓彤1，申永军1,2，王俊锋3

作者信息 +

Parametric optimization of a DVA with amplifying mechanism, inerter and grounded stiffness

YANG Xiaotong1, SHEN Yongjun1,2, WANG Junfeng3

Author information +

文章历史 +

摘要

惯容、放大机构、接地刚度及其组合结构等常用于振动控制中，有着较为良好的减振效果。提出了一种含放大机构和惯容的接地刚度动力吸振器(dynamic vibration absorber，DVA)，该模型以Voigt DVA为基础，引入放大机构、惯容和接地刚度提高系统的减振性能。依据H∞优化准则对吸振器进行了参数优化。首先，建立系统的运动微分方程，基于扩展的固定点理论推导出最优频率比，进而求出系统稳定状态下的最优刚度比及其对应的惯容最佳工作范围，通过基于摄动的方法得到系统近似阻尼比设计公式。最后，通过MATLAB计算数值解验证了解析解的正确性。在简谐激励条件下，与现有的DVA进行对比，证明了该模型具有良好的减振效果，并在随机激励下进一步进行了验证。研究过程和结果对新型动力吸振器的设计和应用有一定的参考意义。
关键词：动力吸振器；参数优化；放大机构；惯容；固定点理论

Abstract

Inerter, amplifying mechanism, grounded stiffness and their combined structures are often used in vibration control, and the better vibration reduction effect can be obtained. A grounded stiffness dynamic vibration absorber (DVA) with amplifying mechanism and inerter is presented. Based on Voigt DVA, the inerter, amplifying mechanism and grounded stiffness are all introduced to improve the vibration damping performance. The parameters optimization are carried out according to H∞ criterion. Firstly, the differential equation of system motion is established, and the optimal frequency ratio is derived based on the extended fixed-point theory. Then the optimal stiffness ratio of the system and the best working range of inerter in stable state are obtained, and the approximate damping ratio of the system is also obtained by using the perturbation-based method. Finally, the correctness of the analytical solution is verified by the numerical solution calculated in MATLAB. Under the condition of simple harmonic excitation, it is proved that this model has great vibration reduction effect by comparing with some existing DVAs. The further verification is fulfilled when the primary system is subjected to random excitation. The investigation procedure and results have certain guiding significance for the design and application of the new DVAs.
Key words: dynamic vibration absorber; parameter optimization; amplifying mechanism; inerter; fixed-point theory

导出引用

杨晓彤1，申永军1,2，王俊锋3. 一种含放大机构、惯容和接地刚度的动力吸振器的参数优化[J]. 振动与冲击, 2022, 41(21): 308-215

YANG Xiaotong1, SHEN Yongjun1,2, WANG Junfeng3. Parametric optimization of a DVA with amplifying mechanism, inerter and grounded stiffness[J]. Journal of Vibration and Shock, 2022, 41(21): 308-215

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