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时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

王长利 赵艳影

王长利, 赵艳影. 时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验. 力学学报, 2023, 55(4): 954-971 doi: 10.6052/0459-1879-23-026
引用本文: 王长利, 赵艳影. 时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验. 力学学报, 2023, 55(4): 954-971 doi: 10.6052/0459-1879-23-026
Wang Changli, Zhao Yanying. Theory and experiment of equal-peak optimization of time delay coupled pendulum tuned mass damper vibrating system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 954-971 doi: 10.6052/0459-1879-23-026
Citation: Wang Changli, Zhao Yanying. Theory and experiment of equal-peak optimization of time delay coupled pendulum tuned mass damper vibrating system. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 954-971 doi: 10.6052/0459-1879-23-026

时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

doi: 10.6052/0459-1879-23-026
基金项目: 国家自然科学基金项目(12072140) 和江西省自然科学基金项目(20202ACBL201003) 资助
详细信息
    通讯作者:

    赵艳影, 教授, 主要研究方向为结构振动与控制. E-mail: yanyingzhao@nchu.edu.cn

  • 中图分类号: O328, TH213.3

THEORY AND EXPERIMENT OF EQUAL-PEAK OPTIMIZATION OF TIME DELAY COUPLED PENDULUM TUNED MASS DAMPER VIBRATING SYSTEM

Funds: The project was supported by the (12345678)and (9876543)
  • 摘要: 摆式调谐质量阻尼器因其便于安装、维修、更换, 且经济实用, 广泛应用于结构减振. 它通过将摆的自振频率调谐到接近主系统的控制频率, 使摆产生与主系统相反的振动, 从而抑制或消除主系统的振动. 本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计, 实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制. 首先, 建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程, 通过对主系统无阻尼的被动减振系统进行等峰优化, 获得了减振系统的最优频率比和质量摆的最优阻尼比. 对于主系统存在阻尼的被动减振系统, 在该优化参数下主系统的幅频响应曲线等峰优化失效. 其次, 对于主系统存在阻尼的时滞反馈优化控制系统, 采用CTCR方法得到了反馈增益系数和时滞的稳定区域. 在保证系统稳定的前提下, 通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制. 再次, 对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析, 表明共振点幅值对反馈增益系数比对时滞更为敏感. 最后, 通过实验分别在频域和时域内对理论结果进行了验证. 研究表明, 通过采用时滞反馈对摆式调谐质量阻尼减振系统进行等峰优化控制, 在较宽的频率区间内抑制了主系统的振幅; 通过控制共振峰和反共振峰的差值, 保证了幅频响应曲线的平坦性.

     

  • 图  1  时滞耦合质量摆减振系统力学模型

    Figure  1.  Mechanical model of time delay coupled pendulum tuned mass damper system

    图  2  主系统阻尼系数对主系统幅频响应曲线的影响

    Figure  2.  Effects of damping coefficient of primary system on amplitude-frequency response curves of primary system

    图  3  稳定性流程图

    Figure  3.  Stability flow chart

    图  4  不同$ {\xi _s} $$g$$\tau $稳定区域

    Figure  4.  Stable region of$g$and$\tau $under different$ {\xi _s} $

    图  5  $ {H_A} - g - \tau $响应曲线

    Figure  5.  Response curves of $ {H_A} - g - \tau $

    图  6  $ {H_A} - g - \tau $响应曲线

    Figure  6.  Response curves of $ {H_A} - g - \tau $

    图  7  $ {H_A} - g - \tau $响应曲线

    Figure  7.  Response curves of $ {H_A} - g - \tau $

    图  8  $ {H_A} - g - \tau $响应曲线

    Figure  8.  Response curves of $ {H_A} - g - \tau $

    图  9  $\left| {{H_{{A}}} - {H_{{C}}}} \right| - g - \tau$响应曲线

    Figure  9.  Response curves of $\left| {{H_{{A}}} - {H_{{C}}}} \right| - g - \tau$

    图  10  $\left| {{H_{{A}}} - {H_{{C}}}} \right| - g - \tau$响应曲线

    Figure  10.  Response curves of $\left| {{H_{{A}}} - {H_{{C}}}} \right| - g - \tau$

    图  11  $ \left| {{H_{A} } - {H_{C} }} \right| - g - \tau $响应曲线

    Figure  11.  Response curves of $ \left| {{H_{A} } - {H_{C} }} \right| - g - \tau $

    图  12  $ \left| {{H_{A} } - {H_{C} }} \right| - g - \tau $响应曲线

    Figure  12.  Response curves of $ \left| {{H_{A} } - {H_{C} }} \right| - g - \tau $

    图  13  第一共振峰反馈增益系数敏感性响应曲线${G_{{{A}}g}}$$ g $

    Figure  13.  Response curve ${G_{{{A}}g}}$$ g $ of sensitivity respect to gain at first peak point

    图  16  第二共振峰时滞敏感性响应曲线${G_{{{B}}\tau }}$$ \tau $

    Figure  16.  Response curve ${G_{{{B}}\tau }}$$ g $ of sensitivity respect to time delay at second peak point

    图  14  第二共振峰反馈增益系数的敏感性响应曲线${G_{{{B}}g}}$$ g $

    Figure  14.  Response curve ${G_{{{B}}g}}$$ g $ of sensitivity respect to gain at second peak point

    图  15  第一共振峰时滞敏感性响应曲线${G_{{{A}}\tau }}$$ \tau $

    Figure  15.  Response curve ${G_{{{A}}\tau }}$$ g $ of sensitivity respect to time delay at first peak point

    图  17  控制参数临界稳定性曲线的CTCR和QPMR法的验证

    Figure  17.  Verification of critical stability curves of control parameters by CTCR and QPMR methods

    图  18  不同主系统阻尼下幅频响应曲线等峰优化结果

    Figure  18.  Equal peak optimization results of amplitude frequency response curve under different primary system

    图  19  不同主系统阻尼下幅频响应曲线等峰优化结果

    Figure  19.  Equal peak optimization results of amplitude frequency response curve under differ rent primary system

    图  20  主系统的时间历程响应曲线

    Figure  20.  Time-history response curves of primary system

    图  21  主系统的时间历程响应曲线

    Figure  21.  Time-history response curves of primary system

    图  22  实验结构照片(1. 非接触激振器, 2. 底座, 3. 主系统质量, 4. 质量摆吸振器, 5. 伺服电机, 6. 控制刚度, 7.8.9. 加速度传感器)

    Figure  22.  Photo of the experimental structure (1. non-contact vibration exciter, 2. base, 3. primary mass, 4. pendulum tuned mass damper, 5. servo motor, 6. controlled stiffness, 7.8.9. acceleration sensors)

    图  23  反馈控制的原理图

    Figure  23.  A schematic of the feedback control

    图  24  外激励频率−固有时滞响应图

    Figure  24.  External excitation frequency−inherent time delay diagram

    图  25  实验和理论的频域对比图

    Figure  25.  Experimental and theoretical comparison in the frequency domain

    图  26  实验的时域图

    Figure  26.  Time domain diagram of the experiment

    图  27  时滞引入时的共振点的时域图

    Figure  27.  Time domain plot of resonance point with time delay

    表  1  实验系统的参数

    Table  1.   Parameters of the experimental system

    m1/kgm2/kgk1/(N·m−1)k2/(N·m−1)
    $4.50$$0.45$$225.13$$1.16$
    c1/(N·m−1·s−1)c2/(N·m−1·s−1)l/m
    $15.42$$3.45$$0.27$
    下载: 导出CSV

    表  2  实验和理论对比表

    Table  2.   Comparison of theoretical and experimental results

    UncontrolledPassive parameter optimizationTime delay feedback control
    first resonance peak${H_{{A} } }$/mm${\varOmega _{{A} } }$/Hz${H_{{A} } }$/mm${\varOmega _{{A} } }$/Hz${H_{{A} } }$/mm${\varOmega _{{A} } }$/Hz
    experiment1.797.000.515.900.186.50
    theory1.588.500.516.500.106.50
    error0.211.5000.600.080
    second resonance peak${H_{{B} } }$/mm${\varOmega _{{B} } }$/Hz${H_{{B} } }$/mm${\varOmega _{{B} } }$/Hz${H_{{B} } }$/mm${\varOmega _{{B} } }$/Hz
    experiment0.319.000.189.00
    theory0.3912.000.1010.0
    error0.083.000.081.00
    下载: 导出CSV

    表  3  理论和实验对应的时滞

    Table  3.   Time delay corresponding to theory and experiment

    Frequency/HzTime delay/ms
    $ \tau $$ {\tau _0} $$ {\tau _{{\text{arti}}}} $
    6.5270120150
    7.7270110160
    9.0270105165
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-01-29
  • 录用日期:  2023-03-22
  • 网络出版日期:  2023-03-23
  • 刊出日期:  2023-04-18

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