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<p>This paper presents a grounded nonlinear energy sink (NES) with negative stiffness attached to a damped primary system, thereby forming a 2-DOF coupled vibration system. The dynamic characteristics of the proposed NES are thoroughly investigated. Using the complexification averaging method, the governing equations for saddle-node bifurcation, codimension-2 bifurcation and Hopf bifurcation are derived. Moreover, the slow invariant manifold of the system is gained, and the necessary conditions for the strongly modulated response (SMR) induced by bifurcations are identified based on the multi-scale method. The vibration mechanism of the system is validated by the analysis of slow invariant manifolds, phase trajectories, time histories and Poincaré maps. A comparison with the grounded damping NES reveals that the introduction of negative stiffness influences the system’s stability and the occurrence of SMR. Furthermore, neglecting primary system damping can lead to misjudgment of system stability. The evaluation of damping dissipation ratio and energy spectrum on vibration reduction effect indicates that negative stiffness facilitates strong energy transfer between the primary system and the NES, thereby enhancing the damping efficiency of the system. These results are of great significance for improving the vibration reduction performance of systems in engineering applications, and provide a theoretical basis for the design of other types of NES.</p>

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Research on Dynamics of a 2-DOF Coupled System with Negative Stiffness

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  • 发表日期：

    2025年6月23日

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  • Hongzhen Zhao,
  • Jing Li,
  • Shaotao Zhu,
  • Yufeng Zhang

摘要

This paper presents a grounded nonlinear energy sink (NES) with negative stiffness attached to a damped primary system, thereby forming a 2-DOF coupled vibration system. The dynamic characteristics of the proposed NES are thoroughly investigated. Using the complexification averaging method, the governing equations for saddle-node bifurcation, codimension-2 bifurcation and Hopf bifurcation are derived. Moreover, the slow invariant manifold of the system is gained, and the necessary conditions for the strongly modulated response (SMR) induced by bifurcations are identified based on the multi-scale method. The vibration mechanism of the system is validated by the analysis of slow invariant manifolds, phase trajectories, time histories and Poincaré maps. A comparison with the grounded damping NES reveals that the introduction of negative stiffness influences the system’s stability and the occurrence of SMR. Furthermore, neglecting primary system damping can lead to misjudgment of system stability. The evaluation of damping dissipation ratio and energy spectrum on vibration reduction effect indicates that negative stiffness facilitates strong energy transfer between the primary system and the NES, thereby enhancing the damping efficiency of the system. These results are of great significance for improving the vibration reduction performance of systems in engineering applications, and provide a theoretical basis for the design of other types of NES.