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

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

上海大学力学与工程科学学院，上海 200444

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
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-28
- 修回日期: 2021-10-27
- 刊出日期: 2022-07-15

Analysis and Simulation of Natural Frequencies of Slightly Curved Pipes

School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, P.R.China

摘要

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所建立的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。
- 管道 /
- Timoshenko /
- 固有频率 /
- Galerkin截断 /
- 数值仿真
Abstract:
For the transverse vibration of slightly curved pipes, a dynamic mechanical model based on the Timoshenko beam theory was established for the 1st time. The natural vibration characteristics of slightly curved pipes under the influence of the fluid flow were analyzed. With the generalized Hamiltonian principle, the governing equation of the transverse vibration of slightly curved pipes under the fluid-structure coupling effect was derived. Based on the Galerkin truncation, the natural frequencies of slightly curved pipes were obtained with the generalized eigenvalue method. Effects of the fluid velocity and the initial deflection on the natural vibration characteristics of the pipe were studied. The equivalent stiffness and damping method-based finite element simulation of the natural vibration of the slightly curved pipe was developed. Then through the finite element numerical simulation, the results of the Galerkin truncation method and the effectiveness of the Timoshenko model were verified. The work shows that, both the fluid velocity and the initial deflection have significant effects on the natural frequencies of slightly curved pipes.
- pipe /
- Timoshenko /
- natural frequency /
- Galerkin truncation /
- numerical simulation

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图 1 微曲管道模型

Figure 1. The physical model for a slightly curved pipe

下载: 全尺寸图片幻灯片

图 2 二节点线（管）单元模型示意图

Figure 2. The model for a 2-node line element

下载: 全尺寸图片幻灯片

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 in a liquid-filled state: (a) the 1st and 2nd natural frequencies; (b) the 3rd and 4th natural frequencies

下载: 全尺寸图片幻灯片

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

Figure 4. Effects of the initial deflection on natural frequencies of the slightly curved pipe with flowing fluid: (a) the 1st and 2nd natural frequencies; (b) the 3rd and 4th natural frequencies

下载: 全尺寸图片幻灯片

图 5 流速对微曲管道固有频率的影响（A₀=0.003 m）：（a）第一和第二阶固有频率；（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 1st and 2nd natural frequencies; (b) the 3rd and 4th natural frequencies

下载: 全尺寸图片幻灯片

图 6 流速对微曲管道固有频率的影响（A₀=0.006 m）：（a）第一和第二阶固有频率；（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 1st and 2nd natural frequencies; (b) the 3rd and 4th natural frequencies

下载: 全尺寸图片幻灯片

表 1 1Cr18Ni9输流管道与流体参数

Table 1. Physical parameters of the 1Cr18Ni9 pipe and fluid

parameter	value
pipe span 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 I_b/m⁴	3.756 × 10⁻¹¹
Poisson’s ratio μ	0.3
fluid density $ {\rho _{\text{f}}} $/(kg/m³)	872.0

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