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不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究

陈依林 杜敬涛 崔海健 赵雨皓 刘杨

陈依林, 杜敬涛, 崔海健, 赵雨皓, 刘杨. 不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究. 力学学报, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-413
引用本文: 陈依林, 杜敬涛, 崔海健, 赵雨皓, 刘杨. 不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究. 力学学报, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-413
Chen Yilin, Du Jingtao, Cui Haijian, Zhao Yuhao, Liu Yang. Performance analysis and stability study of different types of nonlinear vibration absorbers with combined stiffness of horizontal springs. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-413
Citation: Chen Yilin, Du Jingtao, Cui Haijian, Zhao Yuhao, Liu Yang. Performance analysis and stability study of different types of nonlinear vibration absorbers with combined stiffness of horizontal springs. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-11 doi: 10.6052/0459-1879-22-413

不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究

doi: 10.6052/0459-1879-22-413
基金项目: 国家自然科学基金资助项目(11972125)
详细信息
    作者简介:

    杜敬涛, 教授, 主要研究方向: 结构声耦合系统建模与控制. E-mail: dujingtao@hrbeu.edu.cn

  • 中图分类号: O327

PERFORMANCE ANALYSIS AND STABILITY STUDY OF DIFFERENT TYPES OF NONLINEAR VIBRATION ABSORBERS WITH COMBINED STIFFNESS OF HORIZONTAL SPRINGS

  • 摘要: 动力吸振器作为一种振动控制单元被广泛运用于各种工程场合, 但传统的线性吸振器只能实现窄带振动控制. 文章在线性吸振器的基础上引入对称水平弹簧构建线性刚度与非线性刚度相结合的组合刚度非线性吸振器, 以提升吸振器的吸振性能. 考虑实际工程中可能的安装方式, 分别建立水平弹簧接地安装和不接地安装的组合刚度非线性吸振器模型, 利用谐波平衡法结合弧长延拓法解析求解动力学响应, 并与数值结果相互验证, 证明了求解结果的准确性. 随后分析比较两种组合刚度非线性吸振器与线性吸振器以及非线性能量阱之间的吸振性能, 发现水平弹簧接地安装类型的组合刚度非线性吸振器在保留线性吸振器优势的同时又改善其吸振频带窄的缺点, 且与非线性能量阱相比在主共振频率附近的较宽频内吸振性能更优. 在此基础上, 讨论了水平弹簧参数以及吸振器阻尼对主结构振动幅频响应和稳定性的影响, 最后观察分析主结构幅频响应曲线不稳定区内的复杂动力学行为. 研究结果表明合适的设计参数能够使得主结构振动峰值较低的同时, 频响曲线不稳定运动区域的范围也较小.

     

  • 图  1  线性吸振器两端安装水平弹簧

    Figure  1.  Horizontal springs are installed at both ends of the linear vibration absorber

    图  2  非线性恢复力与刚度特性(a)非线性恢复力曲线 (b)非线性刚度特性曲线

    Figure  2.  Nonlinear restoring force and stiffness characteristics (a) Nonlinear restoring force curve (b) Nonlinear stiffness characteristic curve

    图  3  水平弹簧的不同安装形式

    Figure  3.  Different installation forms of horizontal spring

    图  4  解析解与数值解结果验证

    Figure  4.  Verification of analytical and numerical results

    图  5  两种安装形式的幅频特性曲线比较

    Figure  5.  Comparison of amplitude-frequency characteristic curves of two installation forms

    图  6  与线性吸振器的比较

    Figure  6.  Comparison with linear vibration absorber

    图  7  与本质非线性吸振器的比较

    Figure  7.  Comparison with intrinsically nonlinear vibration absorber

    图  8  水平弹簧刚度变化的影响

    Figure  8.  Influence of horizontal spring stiffness change

    图  9  水平弹簧预压缩长度变化的影响

    Figure  9.  Influence of horizontal spring pre-compression length change

    图  10  阻尼变化的影响

    Figure  10.  Influence of damping variation

    图  11  模型A频响曲线

    Figure  11.  Frequency response curve of model A

    图  12  不同观测点下的时域图、相轨迹和庞加莱点

    Figure  12.  Time domain diagram, phase trajectory and Poincare point under different observation points

    表  1  系统模型参数表

    Table  1.   Table of model system parameters

    ParameterVariableValue
    main massm1/ kg100
    main structure stiffnessk1/(N·m−1)4 × 105
    main structure dampingc1/(Ns·m−1)253
    mass of vibration absorberm2/ kg10
    vertical spring stiffnessk2/(N·m−1)1.47 × 105
    vibration absorber dampingc2/(Ns·m−1)50
    horizontal spring stiffnessk3/(N·m−1)4.8 × 105
    original lengthl0/m0.04
    precompression lengthl/m0.036
    external excitation amplitudeF0/N140
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  • 收稿日期:  2022-09-05
  • 录用日期:  2022-11-10
  • 网络出版日期:  2022-11-15

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