含放大机构的三要素型动力吸振器的H&infin;优化

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (5) : 158-165.

论文

含放大机构的三要素型动力吸振器的H∞优化

周子博1,申永军1,2,杨绍普1,2

作者信息 +

H∞ optimization of 3-factor type dynamic vibration absorber with amplification mechanism

ZHOU Zibo1, SHEN Yongjun1,2, YANG Shaopu1,2

Author information +

文章历史 +

摘要

提出了一种含放大机构的三要素型动力吸振器模型，研究了基于H∞优化准则的系统参数最优解析解。首先，将三要素型黏弹性模型与放大机构引入动力吸振器中，通过拉氏变换得到了系统的解析解。随后，以系统的解析解为研究对象发现该系统存在独立于阻尼比的三个固定点，利用固定点理论将三个固定点调到同一高度得到了动力吸振器的最优调谐比和最优刚度比设计公式。最后依据H∞优化准则通过最小化幅频曲线的峰值得到了系统最优阻尼比设计公式，并通过数值仿真验证了解析解的正确性。与三种经典动力吸振器在简谐激励下进行了对比，证明了本文模型有更好的吸振效果。

Abstract

A new kind of three-element type dynamic vibration absorber (DVA) with force amplification element is presented, where the optimal analytical solution is studied based on H∞ optimization principle. At first, the three-element type viscoelastic model and amplification element are introduced into the dynamic vibration absorber, and the analytical solution is obtained by the Laplace transform method. Then, three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimal tuning ratio and optimal stiffness ratio of the dynamic vibration absorber are obtained by adjusting the three fixed points to the same height according to the fixed-point theory. Furthermore, the optimal damping ratio is obtained by minimizing the maximum value of the amplitude-frequency curves according to H∞ optimization principle. The correctness of the analytical results is verified by the comparison with numerical simulation. In addition, compared with other three traditional DVAs under harmonic excitation, the results show that the three-element type dynamic vibration absorber with force amplification element has better performance of vibration absorption.

导出引用

周子博1,申永军1,2,杨绍普1,2. 含放大机构的三要素型动力吸振器的H∞优化[J]. 振动与冲击, 2022, 41(5): 158-165

ZHOU Zibo1, SHEN Yongjun1,2, YANG Shaopu1,2. H∞ optimization of 3-factor type dynamic vibration absorber with amplification mechanism[J]. Journal of Vibration and Shock, 2022, 41(5): 158-165

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