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

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

张博^{1, 2,},
史天姿¹,
张贻林³,
孙东生¹,
袁从敏¹,
丁虎²,
陈立群^2, ,

1.
长安大学理学院，西安 710064
2.
上海大学上海市应用数学和力学研究所，上海 200072
3.
台山核电合营有限公司，广东台山 529228

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
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- 被引次数: 0
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

Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid

1.
School of Sciences, Chang’an University, Xi’an 710064, P.R.China
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
3.
Taishan Nuclear Power Joint Venture Co. , Ltd. , Taishan, Guangdong 529228, P.R.China

摘要

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。
- 旋转 /
- 输液管 /
- 自由振动 /
- 假设模态法 /
- Lagrange方程
Abstract:
The dynamic model was built for rotating pipes conveying fluid based on the Lagrange principle and the assumed mode method. The eigenvalue problem of the system was solved via the method of “reducing the order and increasing the dimension”. The free vibration characteristics of the rotating pipe conveying fluid were analyzed. The variations of the eigenvalue trajectories with the fluid velocity were illustrated under different tip masses and rotating speeds. The effects of system parameters on the critical fluid velocity were revealed. It is found that, the flowing fluid has significant effects on the dynamic characteristics of the rotating pipe. Different internal resonances between the 1st several modes of the system could exist under certain parameter conditions. The work reveals rich dynamic phenomena of the rotating pipe conveying fluid.
- rotation /
- pipe conveying fluid /
- free vibration /
- assumed mode method /
- Lagrange equation

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图 1 旋转输液管动力学模型

Figure 1. The sketch for a rotating pipe conveying fluid

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

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

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

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

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

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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)

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图 6 矩阵C和G对系统第一阶固有频率的影响 (Ω^* = 4，T_m^* = 0.2)

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

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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，T_m^* = 0.2)

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

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表 1 系统参数设置

Table 1. System parameter values

L/m	E/Pa	r/m	R_out/m	R_in/m	ρ_p/(kg·m⁻³)	ρ_f/(kg·m⁻³)
1	4.957×10⁷	0.5	0.025	0.02	2 766	1 000

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表 2 系统第一阶无量纲固有频率本文计算值与文献对比(ρ_f = 0)

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

	Ω^* = 2			Ω^* = 10
	r/L = 0	r/L = 1	r/L = 5	r/L = 0	r/L = 1	r/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

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