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旋转输液管动力稳定性理论分析

张博 史天姿 张贻林 孙东生 袁从敏 丁虎 陈立群

张博,史天姿,张贻林,孙东生,袁从敏,丁虎,陈立群. 旋转输液管动力稳定性理论分析 [J]. 应用数学和力学,2022,43(2):166-175 doi: 10.21656/1000-0887.420135
引用本文: 张博,史天姿,张贻林,孙东生,袁从敏,丁虎,陈立群. 旋转输液管动力稳定性理论分析 [J]. 应用数学和力学,2022,43(2):166-175 doi: 10.21656/1000-0887.420135
ZHANG Bo, SHI Tianzi, ZHANG Yilin, SUN Dongsheng, YUAN Congmin, DING Hu, CHEN Liqun. Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid[J]. Applied Mathematics and Mechanics, 2022, 43(2): 166-175. doi: 10.21656/1000-0887.420135
Citation: ZHANG Bo, SHI Tianzi, ZHANG Yilin, SUN Dongsheng, YUAN Congmin, DING Hu, CHEN Liqun. Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid[J]. Applied Mathematics and Mechanics, 2022, 43(2): 166-175. doi: 10.21656/1000-0887.420135

旋转输液管动力稳定性理论分析

doi: 10.21656/1000-0887.420135
基金项目: 国家自然科学基金(11702033;11872159);中央高校基本科研业务费(300102120166);上海市教委创新项目(2017-01-07-00-09-E00019);陕西省省级大学生创新创业训练计划(S202010710245;S202010710246);陕西省自然科学基金 (2022JQ-019;2020JQ-345;2021JQ-216)
详细信息
    作者简介:

    张博(1989—),男,副教授,博士,硕士生导师(E-mail:zhang_bo@chd.edu.cn)

    陈立群(1963—),男,教授,博士,博士生导师(通讯作者. E-mail:lqchen@shu.edu.cn)

  • 中图分类号: O32

Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid

  • 摘要:

    基于Lagrange原理和假设模态法建立了旋转输液管的动力学模型。通过降阶升维的方法求解系统的特征值问题,并分析了旋转输液管自由振动特性。得到了不同端部集中质量和转速下,系统特征值随流速升高的演变轨迹。揭示了临界流速随系统参数的变化规律。研究发现,内部流体的流动对旋转输液管动力学特性存在显著影响。在某些参数组合下,系统低阶模态能够形成不同形式的内共振关系。预示了旋转输液管模型蕴含丰富的动力学现象。

  • 图  1  旋转输液管动力学模型

    Figure  1.  The sketch for a rotating pipe conveying fluid

    图  2  不同试探函数个数下前三阶特征根轨迹曲线 (Tm* = 0,Ω* = 0):(a) N1 = N2 = 5;(b) N1 = N2 = 8;(c) N1 = N2 = 10;(d) N1 = N2 = 12

    Figure  2.  The trajectories of the 1st 3 eigenvalues for different trail function numbers (Tm* = 0, Ω* = 0): (a) N1 = N2 = 5; (b) N1 = N2 = 8; (c) N1 = N2 = 10; (d) N1 = N2 = 12

    图  3  转速对特征根轨迹的影响 (Tm* = 0):(a) Ω* = 4;(b) Ω* = 8;(c) Ω* = 12

    Figure  3.  Effects of the rotating speed on the eigenvalue trajectories (Tm* = 0): (a) Ω* = 4; (b) Ω* = 8; (c) Ω* = 12

    4  端部集中质量对特征根轨迹的影响 (Ω* = 4):(a) Tm* = 0.2;(b) Tm* = 0.4;(c) Tm* = 0.6

    4.  Effects of the tip mass on the eigenvalue trajectories (Ω* = 4): (a) Tm* = 0.2; (b) Tm* = 0.4; (c) Tm* = 0.6

    图  5  不同端部集中质量下临界流速随转速的变化规律 (Ω* = 4)

    Figure  5.  Variations of the critical fluid velocity with the rotating speed for different tip masses (Ω* = 4)

    图  6  矩阵CG对系统第一阶固有频率的影响 (Ω* = 4,Tm* = 0.2)

    Figure  6.  The effects of matrices C and G on the system 1st natural frequency (Ω* = 4, Tm* = 0.2)

    图  7  旋转输液管前三阶固有频率随流体流速的变化规律 (Ω* = 2,Tm* = 0.2)

    Figure  7.  The variations of the 1st 3 natural frequencies of the rotating pipe (Ω* = 2, Tm* = 0.2)

    表  1  系统参数设置

    Table  1.   System parameter values

    L/mE/Par/mRout /mRin /mρp /(kg·m−3)ρf /(kg·m−3)
    14.957×1070.50.0250.022 7661 000
    下载: 导出CSV

    表  2  系统第一阶无量纲固有频率本文计算值与文献对比(ρf = 0)

    Table  2.   Comparison of the 1st natural frequencies obtained from the present study and the reference (ρf = 0)

    Ω* = 2 Ω* = 10
    r/L = 0r/L = 1r/L = 5 r/L = 0r/L = 1r/L = 5
    this paper ω* 3.619 4.397 6.642 4.951 12.996 27.152
    ref. [33] ω* 3.62 4.40 6.64 4.97 13.1 27.3
    error δ/% 0.028 0.068 0.030 0.382 0.794 0.542
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-17
  • 录用日期:  2021-06-17
  • 修回日期:  2021-07-03
  • 网络出版日期:  2021-12-30
  • 刊出日期:  2022-02-01

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