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微曲输流管道振动固有频率分析与仿真

袁嘉瑞 丁虎 陈立群

袁嘉瑞,丁虎,陈立群. 微曲输流管道振动固有频率分析与仿真 [J]. 应用数学和力学,2022,43(7):1-9 doi: 10.21656/1000-0887.420299
引用本文: 袁嘉瑞,丁虎,陈立群. 微曲输流管道振动固有频率分析与仿真 [J]. 应用数学和力学,2022,43(7):1-9 doi: 10.21656/1000-0887.420299
Jiarui YUAN, Hu DING, Liqun CHEN. Analysis and Simulation of Natural Frequencies of a Slightly Curved Pipe[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420299
Citation: Jiarui YUAN, Hu DING, Liqun CHEN. Analysis and Simulation of Natural Frequencies of a Slightly Curved Pipe[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420299

微曲输流管道振动固有频率分析与仿真

doi: 10.21656/1000-0887.420299
基金项目: 国家杰出青年科学基金(12025204)
详细信息
    作者简介:

    袁嘉瑞(1998—),男,硕士生 (E-mail:yjr199827@qq.com

    丁虎(1978—),男,研究员,博士,博士生导师(通讯作者. E-mail:dinghu3@shu.edu.cn

  • 中图分类号: O32

Analysis and Simulation of Natural Frequencies of a Slightly Curved Pipe

  • 摘要: 首次建立了基于Timoshenko梁理论的微曲输流管道横向振动的动力学模型,并分析了流体流动影响下微曲管道横向自由振动的固有特征。采用广义Hamilton原理,导出了考虑流体影响的微曲管道横向振动的控制方程,通过Galerkin截断对控制方程离散化,再由广义本征值问题得到管道横向振动的固有频率,并研究了液体流速和弯曲幅度对管道横向固有振动特征的影响。发展了基于等效刚度和等效阻尼方法的考虑流体影响的微曲管道振动分析的有限元仿真计算方法,并通过有限元软件实现数值仿真,验证了Galerkin截断的分析结果以及建立的Timoshenko微曲管道动力学模型的有效性。研究表明,流体的流速以及管道的弯曲幅度对管道横向振动固有频率均有显著影响。
  • 图  1  微曲管道模型

    Figure  1.  Physical model of slightly curved pipe

    图  2  二节点线(管)单元模型示意图

    Figure  2.  The model of two-node line element

    图  3  初始中点挠度对充液状态微曲管道固有频率的影响:(a) 第一和第二阶固有频率;(b) 第三和第四阶固有频率

    Figure  3.  Effects of the initial deflection on natural frequencies of the slightly curved pipe at liquid-filled state: (a) the first and second natural frequencies; (b) the third and fourth natural frequencies

    图  4  弯曲幅度对微曲输流管道横向振动固有频率的影响:(a) 第一和二阶固有频率;(b) 第三和第四阶固有频率变化

    Figure  4.  Effects of the initial deflection on natural frequencies of the slightly curved pipe with flowing fluid: (a) the first and second natural frequencies; (b) the third and fourth natural frequencies

    图  5  流速对微曲管道固有频率的影响(A0=0.003 m):(a) 第一和第阶固有频率;(b) 第三和第四阶固有频率

    Figure  5.  Effects of the fluid velocity on natural frequencies of the slightly curved pipe (A0=0.003 m): (a) the first and second natural frequencies; (b) the third and fourth natural frequencies

    图  6  流速对微曲管道固有频率的影响(A0=0.006 m):(a) 第一和第阶固有频率;(b) 第三和第四阶固有频率

    Figure  6.  Effects of the fluid velocity on natural frequencies of the slightly curved pipe (A0=0.006 m): (a) the first and second natural frequencies; (b) the third and fourth natural frequencies

    表  1  1Cr18Ni9输流管道与流体参数

    Table  1.   Physical parameters of 1Cr18Ni9 pipe and fluid

    quantityvalue
    pipe length L/m 1
    pipe density $ {\rho _{\text{p}}} $/(kg/m3) 7 930
    outer diameter D/m 0.006
    pipe thickness h/m 0.000 6
    Young’s modulus E/GPa 194.0
    moment of inertia Ib/m4 3.756 × 10−11
    Poisson’s ratio μ 0.3
    fluid density $ {\rho _{\text{f}}} $/(kg/m3) 872.0
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出版历程
  • 收稿日期:  2021-09-28
  • 录用日期:  2021-11-10
  • 修回日期:  2021-10-27
  • 网络出版日期:  2022-06-02

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