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Background <p>The nonlinear energy sink (NES), as a passive control device, enables targeted energy transfer and delivers superior vibration-reduction performance. Its wide-band absorption, strong robustness, and minimal mass have prompted extensive research, yet the correlation between combined nonlinear damping mechanisms and system stability under random excitations remains underexplored.</p> Methods <p> In this study, the Fokker-Planck-Kolmogorov (FPK) equation of the system is first rigorously derived by the generalized harmonic function method to describe the system behavior under stochastic excitation. The FPK equation is then solved by a fourth-order central finite-difference discretization scheme, and the validity of the solution is confirmed by parallel validation using the Runge-Kutta numerical method. The transfer probability density curves for linearly damped, nonlinearly damped and combined damped NES configurations are then analyzed in comparison. Finally, the stability of the system is parametrically analyzed by mapping the displacement and velocity probability density functions to key system parameters and excitation intensity profiles.</p> Conclusions <p>Combined damping can improve the vibration stability and vibration suppression effect of NES under random excitation, which provides theoretical guidance for the wide use of NES.</p>

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Analysis on Vibration Response of Nonlinear Energy Sink with Combined Damping under Random Excitation

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Jian-chao Zhang,
  • Xing-ke Qi,
  • Jun Wang

摘要

Background

The nonlinear energy sink (NES), as a passive control device, enables targeted energy transfer and delivers superior vibration-reduction performance. Its wide-band absorption, strong robustness, and minimal mass have prompted extensive research, yet the correlation between combined nonlinear damping mechanisms and system stability under random excitations remains underexplored.

Methods

In this study, the Fokker-Planck-Kolmogorov (FPK) equation of the system is first rigorously derived by the generalized harmonic function method to describe the system behavior under stochastic excitation. The FPK equation is then solved by a fourth-order central finite-difference discretization scheme, and the validity of the solution is confirmed by parallel validation using the Runge-Kutta numerical method. The transfer probability density curves for linearly damped, nonlinearly damped and combined damped NES configurations are then analyzed in comparison. Finally, the stability of the system is parametrically analyzed by mapping the displacement and velocity probability density functions to key system parameters and excitation intensity profiles.

Conclusions

Combined damping can improve the vibration stability and vibration suppression effect of NES under random excitation, which provides theoretical guidance for the wide use of NES.