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<p>This study aims to investigate the vibration suppression effectiveness of Nonlinear Energy Sink (NES) on the aeolian vibration in overhead transmission conductors incorporating geometric nonlinearity. The Hamilton’s principle is applied to establish the nonlinear vibration governing equations of the transmission line coupled with NES, and the Galerkin truncation method is used to discretize the partial differential equations into ordinary differential equations. The complex-variable averaging method is applied to derive the modulation equations of the nonlinear coupled system with primary resonance response. Two types of bifurcation boundaries near the primary resonance frequency based on the Routh-Hurwitz criteria is provided. The results demonstrate that numerical verification using the Runge-Kutta method reveals excellent agreement between the numerical and approximate solutions. The NES exhibits excellent performance in suppressing aeolian vibration of transmission conductors. Furthermore, the influence of bending stiffness and sag-to-span ratio on the nonlinear dynamic behavior of the system cannot be ignored. Additionally, rich dynamic phenomena such as saddle-node bifurcation, Hopf bifurcation, and chaotic motion arise near the primary resonance frequency, the Saddle-Node and Hopf bifurcations may coexist.</p>

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Vibration suppression and dynamical bifurcation of aeolian vibration for the transmission conductor based on nonlinear energy sink

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Ziheng Wang,
  • Yangdong Qin,
  • Xiqi Lin,
  • Xiyuan Li,
  • Lingzhi Wang,
  • Zhitao Yan,
  • Xiaochun Nie

摘要

This study aims to investigate the vibration suppression effectiveness of Nonlinear Energy Sink (NES) on the aeolian vibration in overhead transmission conductors incorporating geometric nonlinearity. The Hamilton’s principle is applied to establish the nonlinear vibration governing equations of the transmission line coupled with NES, and the Galerkin truncation method is used to discretize the partial differential equations into ordinary differential equations. The complex-variable averaging method is applied to derive the modulation equations of the nonlinear coupled system with primary resonance response. Two types of bifurcation boundaries near the primary resonance frequency based on the Routh-Hurwitz criteria is provided. The results demonstrate that numerical verification using the Runge-Kutta method reveals excellent agreement between the numerical and approximate solutions. The NES exhibits excellent performance in suppressing aeolian vibration of transmission conductors. Furthermore, the influence of bending stiffness and sag-to-span ratio on the nonlinear dynamic behavior of the system cannot be ignored. Additionally, rich dynamic phenomena such as saddle-node bifurcation, Hopf bifurcation, and chaotic motion arise near the primary resonance frequency, the Saddle-Node and Hopf bifurcations may coexist.