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Further Optimization of Maxwell-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Spring Using Particle Swarm Algorithm

Author

Listed:
  • Yuying Chen

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Jing Li

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Shaotao Zhu

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China
    Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China)

  • Hongzhen Zhao

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

Abstract

Dynamic vibration absorbers (DVAs) are widely used in engineering practice because of their good vibration control performance. Structural design or parameter optimization could improve its control efficiency. In this paper, the viscoelastic Maxwell-type DVA model with an inerter and multiple stiffness springs is investigated with the combination of the traditional theory and an intelligent algorithm. Firstly, the expressions and approximate optimal values of the system parameters are obtained using the fixed-point theory to deal with the H ∞ optimization problem, which can provide help with the range of parameters in the algorithm. Secondly, we innovatively introduce the particle swarm optimization (PSO) algorithm to prove that the algorithm could adjust the value of the approximate solution to minimize the maximum amplitude by analyzing and optimizing the single variable and four variables. Furthermore, the validity of the parameters is further verified by simulation between the numerical solution and the analytical solution using the fourth-order Runge–Kutta method. Finally, the DVA demonstrated in this paper is compared with typical DVAs under random excitation. The timing sequence and variances, as well as the decreased ratios of the displacements, show that the presented DVA has a more satisfactory control performance. The inerter and negative stiffness spring can indeed bring beneficial effects to the vibration absorber. Remarkably, the intelligent algorithm can make the resonance peaks equal in the parameter optimization of the vibration absorber, which is quite difficult to achieve with theoretical methods at present. The results may provide a theoretical and computational basis for the optimization design of DVA.

Suggested Citation

  • Yuying Chen & Jing Li & Shaotao Zhu & Hongzhen Zhao, 2023. "Further Optimization of Maxwell-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Spring Using Particle Swarm Algorithm," Mathematics, MDPI, vol. 11(8), pages 1-28, April.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1904-:d:1125822
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    References listed on IDEAS

    as
    1. Yongjun Shen & Xiaoran Wang & Shaopu Yang & Haijun Xing, 2016. "Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, August.
    2. R. S. Lakes & T. Lee & A. Bersie & Y. C. Wang, 2001. "Extreme damping in composite materials with negative-stiffness inclusions," Nature, Nature, vol. 410(6828), pages 565-567, March.
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    Cited by:

    1. Jian Dong, 2023. "Preface to the Special Issue on “Recent Advances in Swarm Intelligence Algorithms and Their Applications”—Special Issue Book," Mathematics, MDPI, vol. 11(12), pages 1-4, June.

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