基于H2范数的弹性基础上接地负刚度动力吸振最优参数研究

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摘要针对实际工程中弹性基础上接地负刚度动力吸振器的最优参数设计，建立了以无阻尼单自由度系统代表弹性基础的动力学模型，采用H2范数优化准则获得了以外激励到基础的力传递率最小时关于质量比和负刚度比的最优参数解析表达式，开展了简谐激励和随机激励下的效果验证以及不同基础参数下的参数影响分析。结果表明，以控制外激励到基础的力传递率为目标时，最优参数仅取决于吸振质量比和基础与主系统的刚度比，而与基础的质量比无关；当基础与主系统耦合强时，接地负刚度动力吸振依然能实现有效控制，但此时Voigt动力吸振已基本失效。

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	刘冬1
	苏智伟1
	2
	郑智伟1
	杨咏3
	张啸涵1
	李杨1
	黄修长1
	3

关键词 ：弹性基础, 接地负刚度动力吸振, 最优参数, H2范数

Abstract：Aiming at the optimal parameters of the dynamic vibration absorber (DVA) with grounded negative stiffness on the flexible foundation in practical engineering, the dynamic model of the flexible foundation represented by a single degree of freedom (DOF) system without damping is established. The analytical expressions of the optimal parameters about the mass ratio and the negative stiffness ratio are obtained using the H2-optimization method under the optimization object of controlling the force transmissibility to the flexible foundation. The effect is verified under simple harmonic excitation and random excitation and the parameter influence analysis is carried out under different foundation parameters. The results show that when the goal is to control the force transmissibility to the flexible foundation, the optimal parameters only depend on the mass ratio of vibration absorber and the stiffness ratio of the foundation to the main system, but have nothing to do with the mass ratio of the foundation. When the coupling between the foundation and the main system is strong, the DVA with grounded negative stiffness is still effective, however the Voigt DVA would fail.

Key words： flexible foundation DVA with grounded negative stiffness optimal design parameters H2 optimization method

收稿日期: 2022-12-06 出版日期: 2022-12-28

引用本文:

刘冬1，苏智伟1,2，郑智伟1，杨咏3，张啸涵1，李杨1，黄修长1,3. 基于H2范数的弹性基础上接地负刚度动力吸振最优参数研究[J]. 振动与冲击, 2022, 41(24): 305-312.
LIU Dong1, SU Zhiwei1,2, ZHENG Zhiwei1, YANG Yong3, ZHANG Xiaohan1, LI Yang1, HUANG Xiuchang1,3. Optimal parameters of dynamic vibration absorber with grounded negative stiffness on a flexible foundation by H2 optimization method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(24): 305-312.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I24/305

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