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 引用本文: 张运法, 孔宪仁. 具有组合非线性阻尼的非线性能量阱振动抑制响应分析. 力学学报, 2023, 55(4): 972-981.
Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 972-981.
 Citation: Zhang Yunfa, Kong Xianren. Analysis on vibration suppression response of nonlinear energy sink with combined nonlinear damping. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 972-981.

## ANALYSIS ON VIBRATION SUPPRESSION RESPONSE OF NONLINEAR ENERGY SINK WITH COMBINED NONLINEAR DAMPING

• 摘要: 非线性能量阱是一种振动能量吸收装置, 其在结构振动抑制中具有十分重要的作用. 文章对具有组合非线性阻尼非线性能量阱的系统进行振动抑制相关的分析. 首先对具有组合非线性阻尼非线性能量阱的系统进行理论模型的描述, 对系统模型的运动方程利用复变量平均法进行推导, 得到系统的慢变方程. 其次对系统的慢变方程运用多尺度法进行强调制响应的分析, 通过对系统进行慢不变流形和相轨迹的研究, 描述系统强调制响应发生的条件基础. 此外, 还利用一维映射对系统进行分析, 揭示外激励幅值对强调制响应存在时频率失谐系数取值区间的影响规律. 最后利用能量谱、时间响应和庞加莱映射对耦合组合非线性阻尼非线性能量阱系统进行了振动抑制的相关研究, 揭示组合非线性阻尼的非线性能量阱不同阻尼比、阻尼和刚度对其振动抑制效果的影响规律, 得出组合非线性阻尼非线性能量阱和主结构响应存在一致性的现象, 并验证所提出的组合非线性阻尼非线性能量阱模型具有较好的振动抑制能力.

Abstract: Nonlinear energy sink is a kind of vibration energy absorption device, which plays an important role in vibration suppression of structure. In this paper, the correlation analysis of vibration suppression for a system with combined nonlinear damping nonlinear energy sink is carried out. Firstly, the theoretical model of the system with combined nonlinear damping nonlinear energy sink is described. The motion equations of the system model are derived by using the complex variable average method, and the slow variable equations of the system are obtained. Secondly, the slow variable equations of the system are analyzed by using the multi-scale method. By studying the slow invariant manifold and phase trajectories of the system, the condition basis of the strongly modulated response of the system is described. In addition, the influence law of the external excitation amplitude on the frequency detuning coefficient interval in the presence of the strongly modulated response is revealed by analyzing the system with one-dimensional mapping. Finally, the energy spectrum, time response and Poincare mapping are applied to study the vibration suppression of the system with combined nonlinear damping nonlinear energy sink, the influence law of different damping ratio, damping and stiffness of nonlinear energy sink on its vibration suppression effect is revealed. Meanwhile, it is found that the response of the nonlinear energy sink with combined nonlinear damping is consistent with that of the main structure. In addition, it is verified that the nonlinear energy sink with combined nonlinear damping proposed in this study has good vibration suppression ability.

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