楼京俊, 李爽, 柴凯, 卢锦芳. 非线性能量阱振动抑制效果理论分析与试验研究[J]. 工程力学, 2022, 39(6): 202-211. DOI: 10.6052/j.issn.1000-4750.2021.03.0224
引用本文: 楼京俊, 李爽, 柴凯, 卢锦芳. 非线性能量阱振动抑制效果理论分析与试验研究[J]. 工程力学, 2022, 39(6): 202-211. DOI: 10.6052/j.issn.1000-4750.2021.03.0224
LOU Jing-jun, LI Shuang, CHAI Kai, LU Jin-fang. THEORETICAL AND TEST RESEARCH ON THE VIBRATION SUPPRESSION EFFECT OF NONLINEAR ENERGY SINK[J]. Engineering Mechanics, 2022, 39(6): 202-211. DOI: 10.6052/j.issn.1000-4750.2021.03.0224
Citation: LOU Jing-jun, LI Shuang, CHAI Kai, LU Jin-fang. THEORETICAL AND TEST RESEARCH ON THE VIBRATION SUPPRESSION EFFECT OF NONLINEAR ENERGY SINK[J]. Engineering Mechanics, 2022, 39(6): 202-211. DOI: 10.6052/j.issn.1000-4750.2021.03.0224

非线性能量阱振动抑制效果理论分析与试验研究

THEORETICAL AND TEST RESEARCH ON THE VIBRATION SUPPRESSION EFFECT OF NONLINEAR ENERGY SINK

  • 摘要: 针对潜艇机械设备周期性运转产生的宽频线谱难以消除问题,开展了简谐激励下非线性能量阱振动抑制效果与结构参数优化研究。建立机械设备耦合非线性能量阱的动力学模型,利用增量谐波平衡法、弧长延拓法以及Floquet理论分析了系统周期解及其稳定性;以系统振动能量为评价准则,探讨了阻尼、质量比和刚度3个参数对非线性能量阱振动抑制效果的影响规律;进一步,在质量比 \varepsilon = 0.05 时,通过局部优化得到了非线性能量阱阻尼与刚度区间,并对振动抑制效果鲁棒性进行了研究。理论研究表明:增量谐波平衡法、弧长延拓法以及Floquet理论三者相结合,与Runge-Kutta法计算结果吻合良好,能够有效构建耦合系统周期解完整图像;弱阻尼是非线性能量阱具备良好吸振效果的先决条件,对于参数优化后的非线性能量阱,在外界激励频率 \pm 20%以及激励幅值 \pm 50%变化范围内都具备良好的振动抑制效果,鲁棒性较佳。设计了一种可垂向承载的柔性铰链型非线性能量阱原理样机,并开展了台架试验,验证了理论研究成果的正确性。

     

    Abstract: Aiming at eliminating the broadband line spectrum generated by the periodic rotation of submarine mechanical equipment, the vibration suppression effect was investigation and the structural parameter optimization of nonlinear energy sink (NES) were carried out under harmonic excitation. The dynamic model of mechanical equipment coupled with the nonlinear energy sink was established, and the periodic motion and stability of the coupled system were analyzed by incremental harmonic method, arc-length continuation method and Floquet theory. The influence of damping, mass ratio and stiffness on the vibration suppression effect of the nonlinear energy sink was discussed by taking the system vibration energy as evaluation criterion. Furthermore, the optimized damping and stiffness were obtained through local optimization algorithm, also the robustness of the vibration suppression effect was studied. The results show that the proposed method is in good agreement with Runge-Kutta numerical method, which can effectively construct the complete image of the coupled system periodic solution. Besides, weak damping is a prerequisite for a nonlinear energy sink to have good vibration suppression effect and robustness within a range of 20% of excitation frequency and of 50% amplitude after parameter optimization. A NES, parallel with vertical linear springs and constituted by flexible hinges under preloaded state, was proposed and related test research was also carried out to verify the theoretical findings.

     

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