输液直管道流-固耦合振动响应计算方法与应用

田瑞; 常亮; 韩涛; 聂小华

doi:10.21656/1000-0887.440291

输液直管道流-固耦合振动响应计算方法与应用

doi: 10.21656/1000-0887.440291

田瑞^{1, 2,},
常亮^{1, 2},
韩涛^{1, 2},
聂小华^{1, 2}

1.
中国飞机强度研究所，西安 710065
2.
强度与结构完整性全国重点实验室，西安 710065

详细信息

作者简介:
田瑞(1993—)，男，工程师，硕士(通讯作者. E-mail: 458519989@qq.com)

中图分类号: V214
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- 文章访问数: 64
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- 被引次数: 0
出版历程
- 收稿日期: 2023-09-26
- 修回日期: 2024-02-22
- 刊出日期: 2024-12-01

The Calculation Method and Application of Fluid-Solid Coupling Vibration Responses of Straight Infusion Pipeline

TIAN Rui^{1, 2
,},
CHANG Liang^{1, 2},
HAN Tao^{1, 2},
NIE Xiaohua^{1, 2}

1.
Aircraft Strength Research Institute of China, Xi'an 710065, P.R.China
2.
National Key Laboratory of Strength and Structural Integrity, Xi'an 710065, P.R.China

摘要

摘要: 输液管道系统中存在液体压力脉动和管道结构的高度非线性耦合效应，在外激励作用下将产生剧烈的耦合振动现象，严重时会导致输液管道及连接结构失效.针对输液管道流-固耦合振动响应解析方法缺乏，研究了基于微分变换法(DTM)求解含复杂支承的输液管道系统动力学特性及振动响应理论，基于Bernoulli-Euler梁理论建立了跨中含复杂弹性支承的输液直管道流-固耦合振动微分方程，详细推导了基于DTM计算简支、含附加弹性支承输液直管道系统固有频率、位移响应及支承约束反力的表达式，研究了输液管道内压强、流速及附加支承刚度和位置对管道系统固有频率、支承约束反力的影响，并基于结构有限元分析方法验证了DTM的计算精度.研究表明：采用DTM计算含复杂支承输液管道系统流-固耦合振动特性及响应的精度高、适用性强，尤其在复杂边界以及跨中含有附加支承管道系统振动响应计算方面具有明显的优势，基于DTM可以便捷计算流固耦合管道系统强迫振动中的力学响应，为管道及其连接结构的设计提供理论依据.
- 输液直管道 /
- 微分变换法 /
- 流-固耦合 /
- 弹性支承 /
- 振动响应
Abstract: There is a highly nonlinear coupling effect between liquid pressure pulsation and pipeline structure in the infusion pipeline system. Severe coupling vibration will occur under external excitation, which will lead to the failure of the infusion pipeline and connection structure. In view of the lack of analytical methods for the fluid-solid coupling vibration responses of the infusion pipeline, the dynamic characteristics and vibration response theory for the infusion pipeline system with complex supports were given based on the differential transformation method (DTM), and the fluid-solid coupling vibration differential equation for the straight infusion pipeline with complex elastic supports within the span was established based on the Bernoulli-Euler beam theory. The expressions based on the DTM for calculating natural frequencies, displacement responses and support constraint reactions of the pipeline system with the simple support and additional elastic supports were derived in detail. The influences of the internal pressure, the flow rate, the additional support stiffness and the support position on natural frequencies and support constraint reactions of the pipeline system were studied, and the calculation accuracy of the DTM was verified with the structural finite element analysis method. The research shows that, the application of the DTM in the calculation of fluid-solid coupling vibration characteristics and responses of the infusion pipeline system with complex supports has high accuracy and good applicability, especially in the calculation of vibration responses of the pipeline system with complex boundaries and additional supports within the span. Based on the DTM, the mechanical responses of the fluid-solid coupling pipeline system can be conveniently calculated under forced vibration. It provides a theoretical basis for the design of pipelines and connected structures.
- straight infusion pipeline /
- differential transformation method /
- fluid-solid coupling /
- elastic support /
- vibration response

HTML全文

图 1 简支输液管道系统简化模型

Figure 1. The simplified model for the simple support infusion pipeline system

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图 2 附加单个弹性支承简支输液管道系统简化模型

Figure 2. A simple support infusion pipeline system model with an additional elastic support

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图 3 流速和压强对输液管道系统固有频率的影响

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. Effects of the flow rate and the pressure on natural frequencies of the infusion piping system

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图 4 不同外激励工况下流速和压强对约束反力的影响

Figure 4. Influences of the flow rate and the pressure on restrained reactions under different external excitation conditions

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表 1 DTM中基本数学运算^[19]

Table 1. Basic mathematical operations in the DTM^[19]

original function	conversion function
w(x)=y(x)±z(x)	W(k)=Y(k)±Z(k)
w(x)=Ay(x)	W(k)=AY(k)
$w(x)=\frac{\mathrm{d} y(x)}{\mathrm{d} x} $	W(k)=(k+1)Y(k+1)
$w(x)=\frac{\mathrm{d}^{n} y(x)}{\mathrm{d} x^{n}} $	W(k)=(k+1)(k+2)…(k+n)Y(k+n)
w(x)=y(x)z(x)	$ W(k)=\sum\limits_{l=0}^{k} Y(l) Z(k-l)$
w(x)=x^m	$ W(k)=\delta(k-m)= \begin{cases}1, & k=m \\ 0, & k \neq m\end{cases}$

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表 2 DTM中典型边界条件的转换^[20]

Table 2. Typical boundary conditions and transition conditions in DTM^[20]

boundary type	boundary condition	conversion condition
	η(0)=η″(0)=0 η(1)=η″(1)=0	W(0)=W(2)=0 $\sum\limits_{k=0}^{N} W(k)=\sum\limits_{k=0}^{N} k(k-1) W(k)=0 $
	η(0)=η′(0)=0 η″(1)=η'''(1)=0	W(0)=W(1)=0 $ \sum\limits_{k=0}^{N} k(k-1) W(k)=\sum\limits_{k=0}^{N} k(k-1)(k-2) W(k)=0$
	η(0)=η′(0)=0 η(1)=η″(1)==0	W(0)=W(1)=0 $\sum\limits_{k=0}^{N} W(k)=\sum\limits_{k=0}^{N} k(k-1) W(k)=0 $
	η(0)=η′(0)=0 η(1)=η′(1)=0	W(0)=W(1)=0 $ \sum\limits_{k=0}^{N} W(k)=\sum\limits_{k=0}^{N} k W(k)=0$

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表 3 简支输液管道系统固有频率计算结果

Table 3. Calculation results of natural frequencies of the simple support infusion pipeline system

flow condition		natural frequency f_i/Hz			error δ/%
P/MPa	V_f/(m/s)	i	FEM	DTM	error δ/%
0	0	1	86.772	86.772	0
0	0	2	347.134	346.549	0.17
20	10	1	69.0	69.0	0
20	10	2	330.768	330.189	0.18
30	20	1	57.80	57.80	0
30	20	2	322.1	321.491	0.19

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表 4 输液管道系统简支端约束反力

Table 4. Constraining reactions at the simple support end of the infusion pipeline system

excitation frequency ω_f	flow condition		constrained reaction force R₁/N		error δ/%
excitation frequency ω_f	P/MPa	V_f/(m/s)	FEM	DTM	error δ/%
0.5ω₁	0	0	17.018	17.166	0.87
	20	10	30.914	31.109	0.63
	30	20	58.257	58.852	1
ω₁	0	0	2 526.348	2 527.190	0.03
	20	10	27.528	27.692	0.6
	30	20	17.129	17.343	0.5
1.5ω₁	0	0	6.339	6.242	1.5
	20	10	4.497	4.187	6.7
	30	20	3.808	3.518	7.6

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表 5 等支承约束反力设计

Table 5. The equal support constrained reaction force design

flow condition		ω_f	optimal addition stiffness k/(kN/m)	f₁/Hz	constrained reaction force R_j/N			error δ/%
P/MPa	V_f/(m/s)	ω_f	optimal addition stiffness k/(kN/m)	f₁/Hz	j	DTM	FEM	error δ/%
20	10				1	12.407	12.112	2.38
		0.5ω₁	416.0	110.942	k	12.40	12.435	0.28
					2	12.407	12.112	2.38
					1	30.569	30.410	0.52
		ω₁	347.1	105.260	k	30.540	30.813	0.89
					2	30.569	30.410	0.52
					1	9.224	9.396	1.86
		1.5ω₁	231.8	94.920	k	9.215	9.181	0.37
					2	9.224	9.396	1.86
30	20				1	14.293	14.0	2.05
		0.5ω₁	402.3	103.137	k	14.279	14.330	0.36
					2	14.293	14.0	2.05
					1	55.774	55.925	0.27
		ω₁	332.6	96.927	k	55.722	56.521	1.43
					2	55.774	55.925	0.27
					1	7.144	7.276	1.84
		1.5ω₁	217.5	85.606	k	7.138	7.126	0.17
					2	7.144	7.276	1.84

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