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具有组合非线性阻尼的非线性能量阱振动抑制响应分析

张运法 孔宪仁

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(2): 355-364 doi: 10.6052/0459-1879-22-563
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(2): 355-364 doi: 10.6052/0459-1879-22-563
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(2): 355-364 doi: 10.6052/0459-1879-22-563
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(2): 355-364 doi: 10.6052/0459-1879-22-563

具有组合非线性阻尼的非线性能量阱振动抑制响应分析

doi: 10.6052/0459-1879-22-563
基金项目: 国家自然科学基金资助项目(51875119)
详细信息
    作者简介:

    孔宪仁, 教授, 主要研究方向: 非线性动力学. E-mail:kongxr@hit.edu.cn

  • 中图分类号: O328

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.

     

  • 图  1  具有组合非线性阻尼NES系统的理论模型

    Figure  1.  Theoretical model of a system with combined nonlinear damping NES

    图  2  k23 = 4/3, λ221 = λ223 = 0.2时SIM图, 带箭头的点线表示跳跃轨迹, 虚线表示不稳定部分, 实线表示稳定部分.

    Figure  2.  SIM when k23 = 4/3, λ221 = λ223 = 0.2, the dotted line with arrow represents the jump trajectory, the dotted line stands for the unstable part, and the solid line denotes the stable part

    图  3  λ221 = 0.2, λ223 = 0.2, k23 = 4/3, A = 3时系统的相轨迹图

    Figure  3.  Phase trajectories of the system when λ221 = 0.2, λ223 = 0.2, k23 = 4/3, A = 3

    图  4  A = 3时, δ从−8.7 ~ 31.4变化的系统一维映射图

    Figure  4.  One dimensional mapping of system as δ changes from −8.7 to 31.4 when A = 3

    图  5  k23 = 4/3时, 不同阻尼比及不同阻尼NES的主结构能量谱图

    Figure  5.  The energy spectrum of the main structure of NES with different damping ratios and different damping when k23 = 4/3

    图  6  不同阻尼NES的时间响应和庞加莱映射图, 其中红点表示系统达到稳定状态,

    xN, x1表示NES和主结构的位移, vN, v1代表NES和主结构的速度

    Figure  6.  Time response and poincare mapping of NES with different damping where the red dot indicates that the system reaches steady state, xN, x1 represent the displacement of NES and the main structure, and vN, v1 stand for the velocity of NES and main structure

    图  7  λ223 = 0.3, λ221 = 0.03时, 不同刚度NES的主结构能量谱对比图

    Figure  7.  Comparison of energy spectrum of main structure with different stiffness NES when λ223 = 0.3, λ221 = 0.03

    图  8  不同刚度和不同频率的时间响应和庞加莱映射图

    Figure  8.  Time response and Poincare mapping with different stiffness and different frequencies

    8  不同刚度和不同频率的时间响应和庞加莱映射图(续)

    8.  Time response and Poincare mapping with different stiffness and different frequencies (continued)

    图  9  具有不同NES主结构的能量谱对比图

    Figure  9.  Comparison of energy spectrum of main structures with different NES

    表  1  A变化时SMR存在的δ区间

    Table  1.   δ interval where SMR exists when A changes

    Aδ interval where SMR exists
    A = 2δ ∈ [−7.0, 18.6]
    A = 5δ ∈ [−10.8, 56.3]
    A = 7δ ∈ [−15.3, 80.5]
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-11-28
  • 录用日期:  2023-01-06
  • 网络出版日期:  2022-01-08

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