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<p>In view of the constraint that the traditional nonlinear energy sink only has a strongly modulated response (SMR) in the case of 1:1 main resonance, this paper proposes to solve this problem by employing the lever-type NES (LNES). This paper mainly investigates the dynamic characteristics of a LNES with the amplification effects under harmonic excitation. Firstly, the slow invariant manifold model of the system is established using the complex-averaging method. Later, the amplitude-frequency evolution laws and phase trajectory characteristics of the system solutions under fast and slow time scales are revealed through the method of multiple scales to construct a one-dimensional mapping criterion for the SMR generation. Through bifurcation characteristic analysis in parameter space, critical boundary conditions for Saddle-Node bifurcation and Hopf bifurcation are clarified. Finally, the vibration damping performance of the LNES is analyzed through numerical simulation under harmonic excitation and random Gaussian white noise excitation. Numerical simulations demonstrate that the amplification mechanism in the LNES can significantly expand the excitation amplitude range and frequency bandwidth triggering the SMR, enabling LNES to generate the SMR more easily than traditional NES. In addition, the LNES exhibits excellent vibration suppression performance relative to NES, which is manifested in the fact that its performance enhancement is proportional to the increase of amplification ratio, and has wider applicability under broadband excitation. This study provides a theoretical basis for the parameter optimization and engineering application of nonlinear energy sinks with amplification mechanism.</p>

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Strongly modulated response and bifurcation characteristics of a lever-type nonlinear energy sink

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Yifan Luo,
  • Jianbo Gao,
  • Jian Peng,
  • Hongxin Sun,
  • Shuwen Xue,
  • Zhenyu Luo,
  • Ming Zhang

摘要

In view of the constraint that the traditional nonlinear energy sink only has a strongly modulated response (SMR) in the case of 1:1 main resonance, this paper proposes to solve this problem by employing the lever-type NES (LNES). This paper mainly investigates the dynamic characteristics of a LNES with the amplification effects under harmonic excitation. Firstly, the slow invariant manifold model of the system is established using the complex-averaging method. Later, the amplitude-frequency evolution laws and phase trajectory characteristics of the system solutions under fast and slow time scales are revealed through the method of multiple scales to construct a one-dimensional mapping criterion for the SMR generation. Through bifurcation characteristic analysis in parameter space, critical boundary conditions for Saddle-Node bifurcation and Hopf bifurcation are clarified. Finally, the vibration damping performance of the LNES is analyzed through numerical simulation under harmonic excitation and random Gaussian white noise excitation. Numerical simulations demonstrate that the amplification mechanism in the LNES can significantly expand the excitation amplitude range and frequency bandwidth triggering the SMR, enabling LNES to generate the SMR more easily than traditional NES. In addition, the LNES exhibits excellent vibration suppression performance relative to NES, which is manifested in the fact that its performance enhancement is proportional to the increase of amplification ratio, and has wider applicability under broadband excitation. This study provides a theoretical basis for the parameter optimization and engineering application of nonlinear energy sinks with amplification mechanism.