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 引用本文: 范舒铜, 申永军. 简谐激励下黏弹性非线性能量阱的研究. 力学学报, 2022, 54(9): 2567-2576.
Fan Shutong, Shen Yongjun. Research on a viscoelastic nonlinear energy sink under harmonic excitation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2567-2576.
 Citation: Fan Shutong, Shen Yongjun. Research on a viscoelastic nonlinear energy sink under harmonic excitation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2567-2576.

## RESEARCH ON A VISCOELASTIC NONLINEAR ENERGY SINK UNDER HARMONIC EXCITATION

• 摘要: 黏弹性材料作为一种良好的减振材料, 广泛应用于机械、航空和土木等领域. 本文用黏弹性Maxwell器件代替传统非线性能量阱中的阻尼元件, 提出一种新型的黏弹性非线性能量阱, 并对该模型在简谐激励下的减振性能进行分析. 首先, 根据牛顿第二定律建立系统的动力学方程, 采用谐波平衡法求解系统的幅频响应曲线, 并利用MATLAB中的Runge-Kutta数值方法验证解析解的正确性, 结果吻合良好. 然后, 分析黏弹性非线性能量阱的减振性能和参数的影响. 最后, 分析了不同质量比下非线性刚度比和阻尼比同时变化时减振效果的变化趋势, 并讨论了黏弹性非线性能量阱的最佳取值范围. 研究结果表明: 主系统的最大振幅随着非线性刚度的增加先减小后增大; 当参数选取恰当时, 黏弹性非线性能量阱比传统非线性能量阱的减振效果更优; 另外, 随着质量比的增加, 主系统最大振幅的最小值出现先减小后趋于不变的现象, 且非线性刚度比和阻尼比的最佳取值范围有所增大. 以上结论对黏弹性非线性能量阱的实际应用提供了一定的理论依据.

Abstract: As a kind of good damping material, viscoelastic material is widely used in machinery, aviation, civil engineering and other fields. A new viscoelastic nonlinear energy sink is proposed by replacing the damping element with a viscoelastic Maxwell element in the traditional nonlinear energy sink, and the vibration damping performance of the model under harmonic excitation is investigated. Firstly, the dynamic equation of the system is established according to Newton's second law. The harmonic balance method is adopted to obtain the system amplitude-frequency response curves, and the Runge-Kutta numerical method in MATLAB is applied to verify the correctness of the analytical solution, and it is found that the results are in good agreement. Then, the damping performance of the viscoelastic nonlinear energy sink and the influence of parameters are analyzed. Finally, the variation trend of vibration reduction effect are analyzed when the nonlinear stiffness ratio and damping ratio change at the same time under different mass ratios, and the optimal value range of viscoelastic nonlinear energy sink is discussed. The results show that the maximum amplitude of the primary system first decreases and then increases with the increase of nonlinear stiffness. When the parameters are selected properly, the damping effect of viscoelastic nonlinear energy sink is better than that of traditional nonlinear energy sink. In addition, with the increase of the mass ratio, the minimum value of the maximum amplitude of the primary system first decreases and then tends to remain unchanged, and the optimal range of nonlinear stiffness ratio and damping ratio is greater. The above conclusions provide a theoretical basis for the practical application of the viscoelastic nonlinear energy sink.

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