多点基础激励下的空间输流管路动力学建模与振动分析

杨晨; 孙伟; 季文豪; 刘宝繁; 吕尚

doi:10.13224/j.cnki.jasp.20260063

多点基础激励下的空间输流管路动力学建模与振动分析

doi: 10.13224/j.cnki.jasp.20260063

杨晨^{1, 2,},
孙伟^{1, 2,*, ,},
季文豪^{1, 2},
刘宝繁^{1, 2},
吕尚^{1, 2}

1.
东北大学机械工程与自动化学院，沈阳 110819
2.
东北大学航空动力装备振动及控制教育部重点实验室，沈阳 110819

基金项目: 国家科技重大专项（J2019-Ⅰ-0008-0008）

详细信息

作者简介:
杨晨（2003-），男，硕士生，主要从事充液管路振动特性研究。E-mail：2234051739@qq.com

通讯作者:
孙伟（1975-），男，教授，博士，主要从事机械系统动力学及振动控制研究。E-mail：weisun@mail.neu.edu.cn

中图分类号: V448.2
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- 被引次数: 0
出版历程
- 收稿日期: 2026-02-06
- 网络出版日期: 2026-04-24

Dynamic modeling and vibration analysis of spatial fluid-conveying pipe under multi-point base excitations

Yang Chen^{1, 2
,},
Sun Wei^{1, 2,*
, ,},
Ji Wenhao^{1, 2},
Liu Baofan^{1, 2},
Lyu Shang^{1, 2}

1.
School of Mechanical Engineering & Automation，Northeastern University，Shenyang 110819，China
2.
Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China，Northeastern University，Shenyang 110819，China

摘要

摘要:
航空输流管路系统在多卡箍支撑条件下通常承受多点非一致基础激励，传统的均匀加载模型可能难以准确描述实际的载荷环境。为此，以典型空间输流管路为研究对象，基于传递矩阵法（TMM）开展了多点基础激励下的管路系统动力学建模与振动分析研究。通过引入卡箍约束及空间坐标转换矩阵，将考虑流固耦合（FSI）效应的14方程模型拓展到了多支撑空间输流管路系统；进一步，提出了一种在每一卡箍约束处独立施加基础激励的方法，通过将激励嵌入传递矩阵的链式求解过程，实现了多点基础激励的引入。最后，通过搭建实验系统并结合有限元仿真对创建的模型进行了验证，该模型对前6阶固有频率及第1阶共振响应幅值的预测误差分别在5.30%和7.69%以内，从而证明了建模方法的合理性。在此基础上分析了液压参数和卡箍约束位置对管路系统的影响，结果表明：流体压力主导系统基频下降，且卡箍靠近弯管布置会提升系统刚度从而改变管路系统振动特性。相关结果可为管路系统的减振设计与布局优化提供理论依据。
- 空间管路 /
- 动力学建模 /
- 传递矩阵法 /
- 多点基础激励 /
- 振动分析
Abstract:
Aviation fluid-conveying piping systems are usually subjected to multi-point non-uniform base excitations under multi-clamp support conditions, making it difficult for traditional uniform loading models to accurately describe the actual load environment. To this end, based on the Transfer Matrix Method (TMM), this study conducts dynamic modeling and vibration analysis of pipeline systems subjected to multi-point base excitations, using typical space flow pipelines as the research subject. By introducing clamp constraints and spatial coordinate transformation matrices, the 14-equation model accounting for fluid-structure interaction (FSI) effects was extended to a multi-support spatial flow pipeline system. A method for independently applying base excitations at each clamp constraint location was proposed. By embedding excitations into the chain-solving process of the transfer matrix, it achieved the simulation of multi-point base excitations. Finally, the created model was validated by constructing an experimental system and combining it with finite element simulation. The model's prediction errors for the first six natural frequencies and the first-order resonance response amplitude were within 5.30% and 7.69%, thereby validating the reasonableness of the modeling approach. Based on this, the effects of hydraulic parameters and clamp constraint positions on the piping system were analyzed. The results indicate that fluid pressure dominates the decrease in the system's fundamental frequency, and the placement of clamps near elbows enhances system stiffness, thereby altering the vibration characteristics of the piping system. The relevant results can provide a theoretical basis for vibration reduction design and layout optimization of piping systems.
- space pipeline /
- kinetic modeling /
- transfer matrix method /
- multi-point base excitations /
- vibration analysis

HTML

图 1 多点支撑下空间输流管路系统结构示意图

Figure 1. Schematic structure of spatial fluid-conveying piping system under multi-point supports

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图 2 卡箍约束力学模型

Figure 2. Schematic diagram of the spring constraint model

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图 3 多点基础激励的施加过程

Figure 3. The process of applying multi-point base excitations

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图 4 管路坐标转换位置及原理

Figure 4. Pipe coordinate conversion location and schematic

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图 5 空间输流管路振动实验系统

Figure 5. Vibration experiment system for spatial fluid-conveying pipeline

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图 6 基于实验和理论模型获得的振动响应

Figure 6. Vibration response obtained by experimental and theoretical models

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图 7 管内流体对管路系统振动特性的影响

Figure 7. Influence of fluid flow on the vibration characteristics of the piping system

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图 8 卡箍位置变化示意图

Figure 8. Schematic diagram of clamp position changes

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图 9 卡箍位置对管路系统固有频率的影响

Figure 9. The effect of clamp position on the natural frequency of the piping system

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表 1 管体和流体的几何及材料参数

Table 1. Geometrical and material parameters of pipe and fluid

参数	数值	参数	数值
$ {\rho }_{\text{p}}/ （\mathrm{kg}/{\mathrm{m}}^{3}） $	7800	$ {\rho }_{\text{f}}/ （\mathrm{kg}/{\mathrm{m}}^{3}） $	865
$ {R}_{\text{w}} $/mm	35.00	$ \mu $	0.29
D/mm	12.00	$ {D}_{\overline{j}} $/mm	24.00
d/mm	10.00	E/GPa	204.0
e/mm	1.00	G/GPa	79.38
L₀/mm	27.00	L₁/mm	117.0
L₂/mm	15.00	L₃/mm	64.54
L₄/mm	108.6	L₅/mm	64.54
L₆/mm	15.00	L₇/mm	64.82
L₈/mm	95.48	L₉/mm	64.82
L₁₀/mm	15.00	L₁₁/mm	89.00
S₁/mm	29.11	S₂/mm	29.11
S₃/mm	28.64	S₄/mm	28.64

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表 2 辨识得到的卡箍刚度参数

Table 2. Recognized clamp stiffness parameters

参数	数值	参数	数值
$ {K}_{\overline{x}} $/10⁵$ （\mathrm{N}/\mathrm{m}） $	2.98	$ {K}_{{{\theta }_{\overline{x}}}} $/ $ （\mathrm{N}\cdot \mathrm{m}/\mathrm{rad}） $	175
$ {K}_{\overline{y}} $/10⁵$ （\mathrm{N}/\mathrm{m}） $	5.65	$ {K}_{{{\theta }_{\overline{y}}}} $/ $ （\mathrm{N}\cdot \mathrm{m}/\mathrm{rad}） $	387
$ {K}_{\overline{z}} $/10⁶$ （\mathrm{N}/\mathrm{m}） $	9.04	$ {K}_{{{\theta }_{\overline{z}}}} $/ $ （\mathrm{N}\cdot \mathrm{m}/\mathrm{rad}） $	20.6

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表 3 空管状态下管路系统固有频率

Table 3. Natural frequency of the piping system under empty conditions

阶次	理论模型频率/Hz	实验频率/Hz	偏差/%	有限元模型频率/Hz	偏差/%
1	155	152.50	1.61	150.79	2.72
2	159	158.45	0.35	162.88	2.44
3	352	356.40	1.25	360.31	2.36
4	400	413.04	3.26	391.91	2.02
5	603	585.51	2.90	589.58	2.22
6	659	630.72	4.29	670.13	1.60

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表 4 充液状态下管路系统固有频率

Table 4. Natural frequency of the piping system under liquid-filled conditions

阶次	理论模型频率/Hz	实验频率/Hz	偏差/%	有限元模型频率/Hz	偏差/%
1	138	138.16	0.12	133.22	3.46
2	142	144.44	1.72	143.90	1.34
3	315	324.15	2.90	319.07	1.29
4	356	374.88	5.30	347.05	2.51
5	519	538.65	3.79	521.79	0.54
6	586	589.37	0.58	592.40	1.09

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表 5 辨识得到的卡箍阻尼参数

Table 5. Recognized clamp damping parameters

参数	数值	参数	数值
$ {C}_{\overline{x}} $/$ （\mathrm{N}\cdot \mathrm{s}/\mathrm{m}） $	3.3	$ {C}_{{{\theta }_{\overline{x}}}} $/10⁻³$ （\mathrm{N}\cdot \mathrm{m}\cdot \mathrm{s}/\mathrm{rad}） $	3.97
$ {C}_{\overline{y}} $/$ （\mathrm{N}\cdot \mathrm{s}/\mathrm{m}） $	6.0	$ {C}_{{{\theta }_{\overline{y}}}} $/10⁻³$ （\mathrm{N}\cdot \mathrm{m}\cdot \mathrm{s}/\mathrm{rad}） $	8.81
$ {C}_{\overline{z}} $/$ （\mathrm{N}\cdot \mathrm{s}/\mathrm{m}） $	186.0	$ {C}_{{{\theta }_{\overline{z}}}} $/10⁻⁴$ （\mathrm{N}\cdot \mathrm{m}\cdot \mathrm{s}/\mathrm{rad}） $	4.70

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表 6 左卡位置对管路系统振动特性的影响

Table 6. Effect of left-side clamp position on vibration characteristics of the piping system

Y坐标位置/mm	220	260	300	340	380
1阶共振频率/Hz	161	146	131	115	103
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表 7 右卡位置对管路系统振动特性的影响

Table 7. Effect of right-side clamp position on the vibration characteristics of the piping system

Y坐标位置/mm	−200	−240	−280	−320	−360
1阶共振频率/Hz	161	149	133	118	110
位移响应云图

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