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<p>Under varying excitation amplitudes, the bistable nonlinear energy sink (NES) exhibits five distinct response mechanisms: intra-well periodic oscillation, inter-well chaotic oscillation, weakly modulated response (WMR), strongly modulated response (SMR), and inter-well periodic oscillation. Among these, SMR is recognized for achieving the highest vibration absorption efficiency. This paper presents a bistable track NES (BTNES) with nonlinear damping, designed to significantly lower the energy threshold required for SMR, enabling their generation at lower excitation levels and thereby enhancing vibration absorption efficiency. Firstly, the slow invariant manifold (SIM) of the system is derived using the complexification-averaging and multiple scales methods. Based on this analysis, the advantages of the proposed BTNES in terms of energy transfer and response mechanisms are evaluated. Subsequently, global bifurcations, including saddle-node (SN) bifurcations with periodic fixed points and Hopf bifurcations, are analyzed to determine the ranges of stiffness, damping, and other parameters influencing SMR behavior. Finally, the external excitation threshold range for SMR is derived, and the effects of stiffness, damping, and additional parameters on SMR thresholds are systematically investigated, culminating in an optimal parameter design. The findings demonstrate that the BTNES effectively shortens the threshold ranges for intra-well periodic oscillation and inter-well chaotic oscillation, significantly reduces the energy threshold for triggering SMR, and broadens the range of external excitation thresholds required for SMR generation. These results highlight the BTNES's potential for enhanced vibration absorption and improved system performance.</p>

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Nonlinear dynamic characteristics of a bistable track nonlinear energy sink with nonlinear damping

  • 期刊论文

  • 发表日期：

    2025年2月28日

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  • Peng Chen,
  • Ji-Hou Yang,
  • Ning Lv,
  • Xiao-Dong Yang

摘要

Under varying excitation amplitudes, the bistable nonlinear energy sink (NES) exhibits five distinct response mechanisms: intra-well periodic oscillation, inter-well chaotic oscillation, weakly modulated response (WMR), strongly modulated response (SMR), and inter-well periodic oscillation. Among these, SMR is recognized for achieving the highest vibration absorption efficiency. This paper presents a bistable track NES (BTNES) with nonlinear damping, designed to significantly lower the energy threshold required for SMR, enabling their generation at lower excitation levels and thereby enhancing vibration absorption efficiency. Firstly, the slow invariant manifold (SIM) of the system is derived using the complexification-averaging and multiple scales methods. Based on this analysis, the advantages of the proposed BTNES in terms of energy transfer and response mechanisms are evaluated. Subsequently, global bifurcations, including saddle-node (SN) bifurcations with periodic fixed points and Hopf bifurcations, are analyzed to determine the ranges of stiffness, damping, and other parameters influencing SMR behavior. Finally, the external excitation threshold range for SMR is derived, and the effects of stiffness, damping, and additional parameters on SMR thresholds are systematically investigated, culminating in an optimal parameter design. The findings demonstrate that the BTNES effectively shortens the threshold ranges for intra-well periodic oscillation and inter-well chaotic oscillation, significantly reduces the energy threshold for triggering SMR, and broadens the range of external excitation thresholds required for SMR generation. These results highlight the BTNES's potential for enhanced vibration absorption and improved system performance.