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<p>This paper introduces a novel time-delayed bistable nonlinear energy sink (TD-BNES) for efficient vibration suppression. The system equation of a linear oscillator (LO) coupled with the TD-BNES is established. The influence of time-delayed feedback control (TDFC) parameters on the equilibrium stability of the coupled system is analyzed and the stability boundaries are given. By considering the vibration of the LO as the excitation source, a reduced-order model is obtained. The Melnikov method is employed to investigate the threshold conditions for homoclinic bifurcations and chaotic responses of the time-delayed reduced-order system, with theoretical predictions validated by numerical simulations. The results indicate that appropriate TDFC parameters significantly improve the vibration suppression capability of the TD-BNES. Specifically, across a wide range of initial energy levels and external excitation amplitudes, the TD-BNES consistently maintains a high vibration reduction efficiency of approximately 90%. In contrast, under the same varying conditions, the vibration reduction efficiency of the passive BNES drops to only about 50%. Benefiting from the synergistic effects of bistability and TDFC, the proposed TD-BNES proves to be a reliable and efficient vibration reduction strategy.</p>

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Dynamics and vibration suppression of a time-delayed bistable nonlinear energy sink

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Weijie Ding,
  • Zhiqun Liu,
  • Haoyu Liu

摘要

This paper introduces a novel time-delayed bistable nonlinear energy sink (TD-BNES) for efficient vibration suppression. The system equation of a linear oscillator (LO) coupled with the TD-BNES is established. The influence of time-delayed feedback control (TDFC) parameters on the equilibrium stability of the coupled system is analyzed and the stability boundaries are given. By considering the vibration of the LO as the excitation source, a reduced-order model is obtained. The Melnikov method is employed to investigate the threshold conditions for homoclinic bifurcations and chaotic responses of the time-delayed reduced-order system, with theoretical predictions validated by numerical simulations. The results indicate that appropriate TDFC parameters significantly improve the vibration suppression capability of the TD-BNES. Specifically, across a wide range of initial energy levels and external excitation amplitudes, the TD-BNES consistently maintains a high vibration reduction efficiency of approximately 90%. In contrast, under the same varying conditions, the vibration reduction efficiency of the passive BNES drops to only about 50%. Benefiting from the synergistic effects of bistability and TDFC, the proposed TD-BNES proves to be a reliable and efficient vibration reduction strategy.