输流管道弯曲和振动的有限元分析

随岁寒，李成; Sui Suihan; Li Cheng

引 en

输流管道弯曲和振动的有限元分析^*

随岁寒¹
机构：
1. 商丘工学院机械工程学院, 商丘 476000
×
，李成^2,3
机构：
2. 常州工学院汽车工程学院,常州 213032
3. 暨南大学 “重大工程灾害与控制”教育部重点实验室, 广州 510632
×

1. 商丘工学院机械工程学院, 商丘 476000；
2. 常州工学院汽车工程学院,常州 213032；
3. 暨南大学 “重大工程灾害与控制”教育部重点实验室, 广州 510632；

THE FINITE ELEMENT ANALYSIS ON BENDING AND VIBRATION OF THE FLUID-CONVEYING PIPES^*

Sui Suihan¹
Affiliation：
1. School of Mechanical Engineering, Shangqiu Institute of Technology, Shangqiu 476000 ,China
×
，Li Cheng^2,3
Affiliation：
2. School of Automotive Engineering,Changzhou Institute of Technology,Changzhou 213032 ,China
3. MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632 , China
×

1. School of Mechanical Engineering, Shangqiu Institute of Technology, Shangqiu 476000 ,China；
2. School of Automotive Engineering,Changzhou Institute of Technology,Changzhou 213032 ,China；
3. MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632 , China；

通讯作者:

李成,E-mail:licheng@cit.edu.cn

中图分类号:O327;O347

文献标识码:A

文章编号:1672-6553-2022-20(4)-083-08

DOI:10.6052/1672-6553-2021-066

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目录contents

摘要 Abstract
关键词 Keywords
1 物理模型
2 数值算例
2.1 管道弯曲分析
2.2 管道自由振动分析
3 结论
参考文献

摘要

基于Timoshenko梁理论,利用虚功原理严格地建立了输流管道弯曲和振动的有限元方程.利用加速度合成定理推导了流体横向加速度的表达式,计算了两端简支和悬臂两种边界条件下管道受到重力和流体作用时的挠度和转角,分析了流体流速对其影响.两端简支条件下将预应力效应整合到管道应变能中,并讨论了轴向预应力与弯曲挠度的关系.给出了两种边界条件下管道自由振动的前三阶固有频率与流体流速的关系,分析了两端简支条件下管道轴向预应力对振动固有频率的影响.结果表明:两端简支边界条件下,流体速度增大则挠度和转角相应增大,预应力使得挠度和转角减小;前三阶固有频率随流速增大而减小,预应力增大则导致各阶固有频率增大.悬臂边界条件下,流体速度增大则挠度和转角减小,前三阶固有频率随流速增大而减小.

Abstract

Based on the Timoshenko beam theory, the finite element equation for bending and vibration of fluid-conveying pipes is derived using the principle of virtual work. The transverse acceleration of fluid is derived using the theorem of acceleration composition. The deflection and slope of the pipe subjected to the combined actions of gravity and fluid under two boundary conditions are obtained, and the influence of fluid velocity on the deflection and slope is analyzed. Under simply supported boundary constraint at both ends the pre-stress effect is transformed to integrate into the strain energy of the pipe, and the relationship between axial pre-stress and bending deflection is studied. The relationships between the first three natural frequencies and the flow velocity of the pipe under the simply supported and cantilever boundary conditions are obtained, and the influence of the axial pre-stress on the natural frequency under the simply supported condition is presented. The results show that under the condition of simply supported boundary, the deflection and slop increase with the increase of fluid velocity, and the deflection and slop decrease with the increase of pre-stress. With the increase of velocity, the first three natural frequencies decrease, while an increase in pre-stress results in higher natural frequencies. For the cantilever boundary condition, the deflection and slope decrease with the increase of fluid velocity, and the first three natural frequencies decrease with increasing flow velocity.

关键词

输流管道；有限元法；弯曲；自由振动；预应力

Keywords

fluid-conveying pipe ； finite element method ； bending ； free vibration ； pre-stress

引言
输流管道广泛应用于石油化工、航空航天和海洋工程等领域,对其弯曲和振动特性进行研究能够为工程设计、结构优化和应用提供重要参考.输流管道力学问题的研究涉及流体力学、固体力学、动力学与控制等多个学科,已有大量文献研究输流管道的流固耦合振动特性\[1-22\],这些工作主要聚焦在输流管道的动力学响应及稳定性,大部分为宏观输流管道,也涉及微观情形,如输流碳纳米管\[5,7\].然而,以往对输流管道在外力作用下的弯曲变形问题研究不多.Dai和Wang^[4]基于Euler梁模型给出了输流管道的弯曲及振动的控制方程,应用有限元法对控制方程进行求解,其中考虑管道受到集中磁铁引力载荷.为分析管道弯曲问题,本文利用加速度合成定理推导了流体横向加速度的表达式,具体包括三项,即牵连加速度、科氏加速度和向心加速度,具有明确的物理意义.这与2019年田耀宗和蹇开林根据速度场概念推得的形式一致^[23],但途径不同.随后本文基于Timoshenko梁模型推导了重力作用下水平布置输流管道弯曲问题的有限元格式,分析了两端简支和悬臂两种边界条件下流体流速对管道挠度和转角的影响.此外,在两端简支边界条件下还考虑了预应力的因素.
另外,以往应用有限元法研究输流管道流固耦合振动问题的文献相对较少\[1-4\].梁波等^[2]基于Timoshenko梁模型,根据Hamilton原理推导出了输流管道系统动力学有限元方程,分析了输流管道的动力特性与稳态响应.王世忠等^[3]基于Euler梁模型建立了输流管道流固耦合振动的有限元方程,分别讨论了流速、压强变化等因素对管道固有频率的影响.与其不同的是,本文利用虚功原理推导了输流管道系统动力学的有限元方程,考虑到管道在热胀冷缩以及安装等外界条件下承受的轴向预应力,因此动力学方程中计入了预应力因素.此外,与以往研究专门将预应力单列,分析预应力做功不同,本文将预应力作用效应直接体现在总的应变能中.
本文主要框架如下:首先,基于虚功原理建立了输流管道系统的有限元方程;其次,分析了两端简支和悬臂两种边界条件下管道受重力作用时的弯曲以及流速对结果的影响,研究了两端简支边界条件下管道预应力与挠度间的关系;最后,分析了两端简支和悬臂边界条件下管道的自由振动与流速的关系,讨论了在两端简支边界条件下管道预应力与系统固有频率间的关系.
1 物理模型
为建立输流管道流固耦合振动的有限元方程,对输流管道建立如图1所示的坐标系,输流管道在两支撑间的距离为L,受到轴向预应力σ₀,管道内径r₁,外径r₂.
图1 输流管道示意图
Fig.1 Schematic diagram of a fluid-conveying pipe
根据Timoshenko梁理论,梁的位移场可表达为

\begin{matrix} u (x, z, t) = - z ψ (x, t) \\ w (x, z, t) = w (x, t) \end{matrix}

(1)

其中, $u (x, z, t)$ 和 $w (x, z, t)$ 分别是轴向位移和横向位移,ψ为转角,t为时间.正应变ε_xx及切应力γ_xz可表达为^[24]

\begin{matrix} ε_{x x} = - z \frac{\partial ψ}{\partial x} + \frac{1}{2} {(\frac{\partial w}{\partial x})}^{2} + \frac{σ_{0}}{E} \\ γ_{x z} = - ψ + \frac{\partial w}{\partial x} \end{matrix}

(2)

对于各向同性弹性材料,应力在虚应变上所做虚功为

δ U = \int_{0}^{L} \int_{A_{2}} σ_{x x} δ ε_{x x} d A_{2} d x + \int_{0}^{L} \int_{A_{2}} σ_{x z} δ γ_{x z} d A_{2} d x

(3)

如图2所示建立管道微段动坐标系O′x′y′,流体横向加速度可由点的加速度合成定理得到
图2 流体加速度分析
Fig.2 Liquid acceleration analysis

a_{a} = a_{e} + a_{r} + a_{C}

(4)

牵连加速度大小为

a_{e} = \frac{\partial^{2} w}{\partial t^{2}}

(5)

微管段中性面斜率、中性面旋转角速度分别为

θ = \frac{\partial w}{\partial x}

(6)

ω = \frac{\partial^{2} w}{\partial x \partial t}

(7)

从而科氏加速度大小为

a_{C} = 2 v ω = 2 v \frac{\partial^{2} w}{\partial x \partial t}

(8)

管道曲率为

\frac{1}{r} = \frac{|\frac{\partial^{2} w}{\partial x^{2}}|}{{[1 + {(\frac{\partial w}{\partial x})}^{2}]}^{\frac{3}{2}}}

(9)

在小变形条件下 $\frac{\partial w}{\partial x} \approx 0$ ,从而

\frac{1}{r} \approx |\frac{\partial^{2} w}{\partial x^{2}}|

(10)

考虑流体向心加速度方向后得到

a_{r} = \frac{v^{2}}{r} = v^{2} \frac{\partial^{2} w}{\partial x^{2}}

(11)

将式(5)、式(8)和式(11)代入式(4),得到流体横向加速度大小为

a_{a} = a_{e} + a_{r} c o s θ + a_{C} c o s θ \approx \frac{\partial^{2} w}{\partial t^{2}} + v^{2} \frac{\partial^{2} w}{\partial x^{2}} + 2 v \frac{\partial^{2} w}{\partial x \partial t}

(12)

与按照场概念计算结果相同^[23].
管道和流体的惯性力虚功为

\begin{matrix} δ W_{in} = \int_{0}^{L} \int_{A_{2}} (ρ \ddot{u} δ u + ρ \ddot{w} δ w) d A_{2} d x + \\ \int_{0}^{L} \int_{A_{1}} ρ_{f} a_{a} δ w d A_{1} d x \end{matrix}

(13)

其中,A₁代表流体截面,A₂代表管道截面.
外力虚功为

δ W_{E} = \int_{0}^{L} [ρ_{f} A_{1} g + ρ_{b} A_{2} g] δ w d x

(14)

其中,g为重力加速度并假设其方向沿y轴正方向.
将式(3)、式(13)和式(14)代入如下虚功原理表达式

δ U + δ W_{i n} = δ W_{E}

(15)

并略去应变能高阶项得到

\begin{matrix} \int_{0}^{L} E I \frac{\partial ψ}{\partial x} \frac{\partial δ ψ}{\partial x} d x + \int_{0}^{L} \int_{A} κ G (ψ δ ψ - \frac{\partial w}{\partial x} δ ψ - ψ \frac{\partial δ w}{\partial x} + \frac{\partial w}{\partial x} \frac{\partial δ w}{\partial x}) d A_{2} d x + \int_{0}^{L} σ_{0} A_{2} \frac{\partial w}{\partial x} \frac{\partial δ w}{\partial x} d x + \\ \int_{0}^{L} \int_{A_{2}} ρ_{b} I \frac{\partial^{2} ψ}{\partial t^{2}} δ ψ + ρ_{b} \frac{\partial^{2} w}{\partial t^{2}} δ w d A_{2} d x + \int_{0}^{L} ρ_{f} A_{1} (\frac{\partial^{2} w}{\partial t^{2}} δ w + 2 v \frac{\partial^{2} w}{\partial x \partial t} δ w + v^{2} \frac{\partial^{2} w}{\partial x^{2}}) δ w d x = \\ \int_{0}^{L} [ρ_{f} A_{1} g + ρ_{b} A_{2} g] δ w d x \end{matrix}

(16)

采用如下形函数
$w (x, z, t) = [\begin{matrix} H_{1} H_{2} 0 H_{3} H_{4} 0 \end{matrix}] {\{\begin{matrix} w_{1} \frac{\partial w_{1}}{\partial x} ψ_{1} w_{2} \frac{\partial w_{2}}{\partial x} ψ_{2} \end{matrix}\}}^{T} = N {d}$

ψ (x, z, t) = [\begin{matrix} 0 0 N_{1} 0 0 N_{2} \end{matrix}] {\{w_{1} \frac{\partial w_{1}}{\partial x} ψ_{1} w_{2} \frac{\partial w_{2}}{\partial x} ψ_{2}\}}^{T} = M {d}

(17)

其中
$\begin{matrix} N_{1} = 1 - \frac{x}{l}, N_{2} = \frac{x}{l} \\ H_{1} = 1 - \frac{3 x^{2}}{l^{2}} + \frac{2 x^{3}}{l^{3}} \\ H_{2} = x - \frac{2 x^{2}}{l} + \frac{x^{3}}{l^{2}} \\ H_{3} = \frac{3 x^{2}}{l^{2}} - \frac{2 x^{3}}{l^{3}} \\ H_{4} = - \frac{x^{2}}{l} + \frac{x^{3}}{l^{2}} \end{matrix}$
将式(17)代入式(16)得到输流管道系统有限元方程

M {\ddot{d}} + C {\dot{d}} + K {d} = F

(18)

其中,质量矩阵M、陀螺矩阵C、刚度矩阵K和外力矩阵F分别为
$\begin{matrix} M = \int_{0}^{L} \int_{A} (ρ_{b} I M^{T} M + ρ_{b} N^{T} N) d A_{2} d x + \\ \int_{0}^{L} \int_{1} R_{1} ρ_{f} N^{T} N d r d x \\ C = \int_{0}^{L} 2 ρ_{f} v A_{1} N^{T} N_{x} d r d x \end{matrix}$

\begin{matrix} K = \int_{0}^{L} E I M_{x}^{T} M_{x} d x + \int_{0}^{L} \int_{A} κ G (M^{T} M - \\ M^{T} N_{x} - N_{x}^{T} M + N_{x}^{T} N_{x}) d A_{2} d x + \\ \int_{0}^{L} ρ_{f} v^{2} A_{1} N^{T} N_{x x} d x + \int_{0}^{L} \int_{A} σ_{0} N_{x}^{T} N_{x} d A_{2} d x \\ F = \int_{0}^{L} [ρ_{f} A_{1} g + ρ_{b} A_{2} g] N^{T} d x \end{matrix}

(19)

2 数值算例
设管道长度L=8m,弹性模量E=210GPa,泊松比为0.3,密度7850kg/m³;管外壁半径r ₂=0.1885m,内壁半径r₁=0.1825m;流体密度为800kg/m³.
2.1 管道弯曲分析
在分析管道在自重下的弯曲时,将式(18)中与时间相关的项略去,对悬臂管道还须令预应力σ₀=0,得到如下静力学方程

K {d} = F

(20)

其中,刚度矩阵K与无流体管道对比,增加项代表的是管道受到的流体离心力,即式(11).求解式(20)可得管道横向位移和转角.
两端简支边界条件下,管道受重力而产生y正方向的挠度,流体离心力总是垂直于管道且和重力方向相同,因此流体速度越大,管道的挠度和转角越大.图3和图4分别为两端简支管道的挠度和转角,其与流体速度的关系符合理论预测.图5给出了流体速度v=80m/s的条件下轴向预应力的变化对两端简支管道的挠度的影响,可见预应力越大则挠度越小,预应力的存在有效增强了输流管的抗弯刚度.
在悬臂条件下,流体离心力总是和重力方向相反,因此随着流速的增大管道挠度和转角逐渐减小,图6和图7分别为悬臂管道的挠度和转角,其与流体速度的关系符合理论预测.
图3 两端简支管道的挠度(σ₀=0)
Fig.3 Deflection of pipes with simply supported boundary condition (σ₀=0)
图4 两端简支管道的转角(σ₀=0)
Fig.4 Slop of pipes with simply supported boundary condition (σ₀=0)
2.2 管道自由振动分析
略去式(18)中外力矩阵,同样对悬臂管道须令预应力σ₀=0,得到如下自由振动方程

M {\ddot{d}} + C {\dot{d}} + K {d} = 0

(21)

图5 轴向预应力对两端简支管道的挠度的影响
Fig.5 Effect of pre-stress on deflection of simply supported pipes
图6 悬臂管道的挠度
Fig.6 Deflection of cantilever pipes
图7 悬臂管道的转角
Fig.7 Slop of cantilever pipes
求解式(21)得到管道系统各阶振动频率.文献^[11]基于Euler梁理论,利用直接解法得到前三阶固有频率的解析解为

ω_{1} = \sqrt{\frac{E I \frac{π^{4}}{L^{4}} - [ρ_{f} A_{f} v^{2} - σ_{0} π (r_{2}^{2} - r_{1}^{2})] \frac{π^{2}}{L^{2}}}{ρ_{b} I \frac{π^{2}}{L^{2}} + (ρ_{b} A + ρ_{f} A_{f})}}

(22)

ω_{2} = \sqrt{\frac{E I \frac{16 π^{4}}{L^{4}} - [ρ_{f} A_{f} v^{2} - σ_{0} π (r_{2}^{2} - r_{1}^{2})] \frac{4 π^{2}}{L^{2}}}{ρ_{b} I \frac{4 π^{2}}{L^{2}} + (ρ_{b} A + ρ_{f} A_{f})}}

(23)

ω_{3} = \sqrt{\frac{E I \frac{81 π^{4}}{L^{4}} - [ρ_{f} A_{f} v^{2} - σ_{0} π (r_{2}^{2} - r_{1}^{2})] \frac{9 π^{2}}{L^{2}}}{ρ_{b} I \frac{9 π^{2}}{L^{2}} + (ρ_{b} A + ρ_{f} A_{f})}}

(24)

表1给出了简支管道流速为零时的前三阶固有频率与ANSYS所得结果的对比,误差在4%以内,证明本文分析方法有效.图8给出了两端简支管道系统前三阶固有频率与流速的关系,其中虚部代表固有频率,实部表征系统稳定性.当流体速度为220m/s时,第一阶固有频率虚部为零,这一速度可称为临界速度,此时实部开始分岔提示系统失稳,这一失稳形式属于动态失稳,因为系统第一阶模态类似静态弯曲挠度(图3),当流体速度超过临界速度时,过大的流体离心力将对管道造成破坏.本文得出的有限元结果与文献^[11]的结果在速度改变时规律相同,即流体速度越大,各阶固有频率越小,且数值结果一致.表2给出了前三阶固有频率随管道预应力的改变规律,可见随着管道预应力的增大,前三阶固有频率均表现出增大趋势,在管道轴向预应力从-100MPa到100MPa的增大过程中,前三阶固有频率的增加幅度分别为29.46%、5.17%和2.22%.
表3给出了悬臂管道流速为零时的前三阶固有频率与ANSYS所得结果的对比,误差也在4%以内.图9给出了悬臂管道系统前三阶固有频率与流速的关系,可见流体速度增大则各阶频率减小,这一规律与两端简支管道相同,不同在于悬臂支撑条件下各阶固有频率低于两端简支情况.值得一提的是,本文在弯曲部分只考虑重力和流体离心力,而在振动部分还考虑了惯性离心力和科氏力,因此流速的增大使得悬臂输流管道的变形和振动频率均降低.与图8两端简支的边界条件不同,即使流体速度大于临界速度,图9前三阶固有频率的实部都为负,这表示此时系统仍然稳定.针对这一现象,以第一阶模态为例说明如下:输流管道偏离平衡位置振动时,离心力和科氏力与恢复力方向相同,即阻止了振动的发生.第一阶固有频率为零意味着在这些流速数值下不产生第一阶模态振动,因此悬臂管道第一阶固有频率为零的状态可归为静态失稳.
表1 简支管道固有频率对比(v=0m/s)
Table1 Comparisons of natural frequencies of simply supported pipes (v=0m/s)
图8 两端简支管道固有频率与流速关系(σ₀=6MPa)
Fig.8 Natural frequency versus liquid velocity for simply supported pipes (σ₀=6MPa)
表2 简支管道预应力与固有频率的关系(v=100m/s)
Table2 Natural frequency versus pre-stress for simply supported pipes (v=100m/s)
表3 悬臂管道固有频率对比(v=0m/s)
Table3 Comparisons of natural frequencies of cantilever pipes (v=0m/s)
图9 悬臂管道固有频率与流速关系
Fig.9 Natural frequency versus liquid velocity for cantilever pipes
3 结论
根据Timoshenko梁模型并利用虚功原理建立了输流管道弯曲和振动的有限元方程.考虑重力带来的管道弯曲变形和管道预应力效应推导了应力在虚应变上所做虚功,利用加速度合成定理分析了流体的加速度.随后分别分析了两端简支和悬臂边界条件下流速对管道弯曲和振动的影响,在两端简支条件下可退化为基于Euler梁模型的前三阶固有频率的解析表达,并分析了预应力效应.研究总结如下:
(1)两端简支条件下,流速越大,挠度和转角越大,管道轴向预应力增大挠度减小.流速提高,则前三阶固有频率减小,管道轴向预应力增大使得前三阶固有频率增大.
(2)悬臂边界条件下,流速越大,挠度和转角越小;较高的流速使得前三阶固有频率降低.
(3)输流管道作为典型的含有科氏力、离心力的动力学系统,求解得到系统复频率,并从中揭示了系统的稳定性.
参考文献
- [1] 王本利,王世忠,安为民,等.用有限元法分析导管固液耦合振动.哈尔滨工业大学学报,1985(2):11~16(Wang B L,Wang S Z,An W M,et al.An analysis of solid-fluid coupling vibration in piping by finite element method.Journal of Harbin Institute of Technology,1985(2):11~16(in Chinese))
- [2] 梁波,唐家祥.输液管道动力特性与动力稳定性的有限元分析.固体力学学报,1993,14(2):167~170(Liang B,Tang J X.Analysis of the dynamic characteristics and stability of pipes conveying fluid by finite element method.Acta Mechanica Solida Sinica,1993,14(2):167~170(in Chinese))
- [3] 王世忠,刘玉兰,黄文虎.输送流体管道的固—液耦合动力学研究.应用数学和力学,1998(11):46~52(Wang S Z,Liu Y L,Huang W H.Research on solid-liquid coupling dynamics of pipe conveying fluid.Applied Mathematics and Mechanics,1998(11):46~52(in Chinese))
- [4] Dai H L,Wang L.Dynamics and stability of magnetically actuated pipes conveying fluid.International Journal of Structural Stability and Dynamics,2016,16(6):1550026
- [5] Zhang Y W,Zhou L,Fang B,et al.Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid.Acta Mechanica Solida Sinica,2017,30:550~556
- [6] 王忠民,冯振宇,赵凤群,等.弹性地基输流管道的耦合模态颤振分析.应用数学和力学,2000(10):72~80(Wang Z M,Feng Z Y,Zhao F Q,et al.Analysis of coupled mode flutter of pipes conveying fluid on the elastic foundation.Applied Mathematics and Mechanics,2000(10):72~80(in Chinese))
- [7] Wang L.Vibration analysis of fluid-conveying nanotubes with consideration of surface effects.Physica E,2010,43(1):437~439
- [8] 倪樵,黄玉盈,陈贻平.微分求积法分析具有弹性支承输液管的临界流速.计算力学学报,2001,18(2):146~149(Ni Q,Huang Y Y,Chen Y P.Differential quadrature method for analyzing critical flow velocity of the pipe conveying fluid with spring support.Chinese Journal of Computational Mechanics,2001,18(2):146~149(in Chinese))
- [9] 赵凤群,王忠民,冯振宇.三参量固体模型粘弹性输流管道的动力特性分析.固体力学学报,2002,23(4):483~489(Zhao F Q,Wang Z M,Feng Z Y.Analysis of the dynamic behaviors of viscoelastic pipe conveying fluid with three-parameter solid model.Acta Mechanica Solida Sinica,2002,23(4):483~489(in Chinese))
- [10] 刘俊卿,王克林.弹性支承输液管道的临界流速.应用力学学报,2003,20(1):133~135(Liu J Q,Wang K L.Critical flow velocity of pipes conveying fluid with elastic supports.Chinese Journal of Applied Mechanics,2003,20(1):133~135(in Chinese))
- [11] 初飞雪.两端简支输液管道流固耦合振动分析.中国机械工程,2006,17(3):248~251(Chu F X.Liquid-solid coupling vibration analysis of the hinged pipes for fluid transportation.China Mechanical Engineering,2006,17(3):248~251(in Chinese))
- [12] 马小强,向宇,黄玉盈.求解弹性地基上任意支承输液直管稳定性问题的传递矩阵法.工程力学,2004(4):194~198(Ma X Q,Xiang Y,Huang Y Y.A transfer matrix method for solving stability of pipes conveying fluid on elastic foundation with various end supports.Engineering Mechanics,2004(4):194~198(in Chinese))
- [13] 樊丽俭,张瑞平.轴向载荷输流管道的稳定性分析.西北大学学报(自然科学版),2004,34(2):158~162(Fan L J,Zhang R P.Stability of pipe conveying fluid under axial load.Journal of Northwest University(Nature Science Edition),2004,34(2):158~162(in Chinese))
- [14] 王忠民,张战午,李会侠.弹性地基上输送振荡流粘弹性管道的动力稳定性.机械工程学报,2005,41(10):57~60(Wang Z M,Zhang Z W,Li H X.Dynamic stability of viscoelastic pipes conveying pulsating fluid on the elastic foundation.Chinese Journal of Mechanical Engineering,2005,41(10):57~60(in Chinese))
- [15] 李宝辉,高行山,刘永寿,等.两端固支输流管道流固耦合振动的稳定性分析.机械设计与制造,2010(2):105~107(Li B H,Gao H S,Liu Y S,et al.The stability analysis of liquid-filled pipes with fixed bearing at both ends under FSI vibration.Machinery Design & Manufacture,2010(2):105~107(in Chinese))
- [16] 赵千里,孙志礼,柴小冬,等.具有弹性支承输流管路的强迫振动分析.机械工程学报,2017,53(12):186~191(Zhao Q L,Sun Z L,Chai X D,et al.Forced vibration analysis of fluid-conveying pipe with elastic supports.Chinese Journal of Mechanical Engineering,2017,53(12):186~191(in Chinese))
- [17] Tang Y,Yang T.Bi-directional functionally graded nanotubes:fluid conveying dynamics.International Journal of Applied Mechanics,2018,10(4):1850041
- [18] Tang Y,Yang T.Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material.Composite Structures,2018,185:393~400
- [19] Lee H L,Chang W J.Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory.Journal of Physis-Condensed Matter,2009,21(11):115302
- [20] Sheng G G,Wang X.Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads.Composite Structures,2011,93(1):162~170
- [21] Rashidi V,Mirdamadi H R,Shirani E.A novel model for vibrations of nanotubes conveying nanoflow.Computational Materials Science,2012,51(1):347~352
- [22] 王琳,倪樵,黄玉盈.GDQR法用于输流曲管的流致振动研究.动力学与控制学报,2005,3(1):72~77(Wang L,Ni Q,Huang Y Y.GDQR for the analyses of flow-induced vibrations of curved pipes conveying fluid.Journal of Dynamics and Control,2005,3(1):72~77(in Chinese))
- [23] 田耀宗,蹇开林.轴向运动梁的横向振动分析.应用数学和力学,2019,40(10):1081~1088(Tian Y Z,Jian K L.Lateral vibration analysis of axially moving beams.Applied Mathematics and Mechanics,2019,40(10):1081~1088(in Chinese))
- [24] 刘涛,罗梦翔,吴炜,等.有限元法的轴向运动梁的激励功率谱辨识.动力学与控制学报,2016,14(2):92~98(Liu T,Luo M X,Wu W,et al.Identification of excitation power spectrum density for an axially moving beam using finite element method.Journal of Dynamics and Control,2016,14(2):92~98(in Chinese))

基本信息

中图分类号: O327;O347
文献标识码: A
DOI: 10.6052/1672-6553-2021-066
文章编号: 1672-6553-2022-20(4)-083-08

基金信息

国家自然科学基金资助项目(11972240)；
暨南大学“重大工程灾害与控制”教育部重点实验室开放基金(20180930002)资助；
The project supported by the National Natural Science Foundation of China (11972240) ；
the Open Project of MOE Key Lab of Disaster Forecast and Control in Engineering (Jinan University, 20180930002)；

引用信息

稿件历史

收稿日期: 2020-08-07

参考文献

[1] 王本利,王世忠,安为民,等.用有限元法分析导管固液耦合振动.哈尔滨工业大学学报,1985(2):11~16(Wang B L,Wang S Z,An W M,et al.An analysis of solid-fluid coupling vibration in piping by finite element method.Journal of Harbin Institute of Technology,1985(2):11~16(in Chinese))
[2] 梁波,唐家祥.输液管道动力特性与动力稳定性的有限元分析.固体力学学报,1993,14(2):167~170(Liang B,Tang J X.Analysis of the dynamic characteristics and stability of pipes conveying fluid by finite element method.Acta Mechanica Solida Sinica,1993,14(2):167~170(in Chinese))
[3] 王世忠,刘玉兰,黄文虎.输送流体管道的固—液耦合动力学研究.应用数学和力学,1998(11):46~52(Wang S Z,Liu Y L,Huang W H.Research on solid-liquid coupling dynamics of pipe conveying fluid.Applied Mathematics and Mechanics,1998(11):46~52(in Chinese))
[4] Dai H L,Wang L.Dynamics and stability of magnetically actuated pipes conveying fluid.International Journal of Structural Stability and Dynamics,2016,16(6):1550026
[5] Zhang Y W,Zhou L,Fang B,et al.Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid.Acta Mechanica Solida Sinica,2017,30:550~556
[6] 王忠民,冯振宇,赵凤群,等.弹性地基输流管道的耦合模态颤振分析.应用数学和力学,2000(10):72~80(Wang Z M,Feng Z Y,Zhao F Q,et al.Analysis of coupled mode flutter of pipes conveying fluid on the elastic foundation.Applied Mathematics and Mechanics,2000(10):72~80(in Chinese))
[7] Wang L.Vibration analysis of fluid-conveying nanotubes with consideration of surface effects.Physica E,2010,43(1):437~439
[8] 倪樵,黄玉盈,陈贻平.微分求积法分析具有弹性支承输液管的临界流速.计算力学学报,2001,18(2):146~149(Ni Q,Huang Y Y,Chen Y P.Differential quadrature method for analyzing critical flow velocity of the pipe conveying fluid with spring support.Chinese Journal of Computational Mechanics,2001,18(2):146~149(in Chinese))
[9] 赵凤群,王忠民,冯振宇.三参量固体模型粘弹性输流管道的动力特性分析.固体力学学报,2002,23(4):483~489(Zhao F Q,Wang Z M,Feng Z Y.Analysis of the dynamic behaviors of viscoelastic pipe conveying fluid with three-parameter solid model.Acta Mechanica Solida Sinica,2002,23(4):483~489(in Chinese))
[10] 刘俊卿,王克林.弹性支承输液管道的临界流速.应用力学学报,2003,20(1):133~135(Liu J Q,Wang K L.Critical flow velocity of pipes conveying fluid with elastic supports.Chinese Journal of Applied Mechanics,2003,20(1):133~135(in Chinese))
[11] 初飞雪.两端简支输液管道流固耦合振动分析.中国机械工程,2006,17(3):248~251(Chu F X.Liquid-solid coupling vibration analysis of the hinged pipes for fluid transportation.China Mechanical Engineering,2006,17(3):248~251(in Chinese))
[12] 马小强,向宇,黄玉盈.求解弹性地基上任意支承输液直管稳定性问题的传递矩阵法.工程力学,2004(4):194~198(Ma X Q,Xiang Y,Huang Y Y.A transfer matrix method for solving stability of pipes conveying fluid on elastic foundation with various end supports.Engineering Mechanics,2004(4):194~198(in Chinese))
[13] 樊丽俭,张瑞平.轴向载荷输流管道的稳定性分析.西北大学学报(自然科学版),2004,34(2):158~162(Fan L J,Zhang R P.Stability of pipe conveying fluid under axial load.Journal of Northwest University(Nature Science Edition),2004,34(2):158~162(in Chinese))
[14] 王忠民,张战午,李会侠.弹性地基上输送振荡流粘弹性管道的动力稳定性.机械工程学报,2005,41(10):57~60(Wang Z M,Zhang Z W,Li H X.Dynamic stability of viscoelastic pipes conveying pulsating fluid on the elastic foundation.Chinese Journal of Mechanical Engineering,2005,41(10):57~60(in Chinese))
[15] 李宝辉,高行山,刘永寿,等.两端固支输流管道流固耦合振动的稳定性分析.机械设计与制造,2010(2):105~107(Li B H,Gao H S,Liu Y S,et al.The stability analysis of liquid-filled pipes with fixed bearing at both ends under FSI vibration.Machinery Design & Manufacture,2010(2):105~107(in Chinese))
[16] 赵千里,孙志礼,柴小冬,等.具有弹性支承输流管路的强迫振动分析.机械工程学报,2017,53(12):186~191(Zhao Q L,Sun Z L,Chai X D,et al.Forced vibration analysis of fluid-conveying pipe with elastic supports.Chinese Journal of Mechanical Engineering,2017,53(12):186~191(in Chinese))
[17] Tang Y,Yang T.Bi-directional functionally graded nanotubes:fluid conveying dynamics.International Journal of Applied Mechanics,2018,10(4):1850041
[18] Tang Y,Yang T.Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material.Composite Structures,2018,185:393~400
[19] Lee H L,Chang W J.Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory.Journal of Physis-Condensed Matter,2009,21(11):115302
[20] Sheng G G,Wang X.Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads.Composite Structures,2011,93(1):162~170
[21] Rashidi V,Mirdamadi H R,Shirani E.A novel model for vibrations of nanotubes conveying nanoflow.Computational Materials Science,2012,51(1):347~352
[22] 王琳,倪樵,黄玉盈.GDQR法用于输流曲管的流致振动研究.动力学与控制学报,2005,3(1):72~77(Wang L,Ni Q,Huang Y Y.GDQR for the analyses of flow-induced vibrations of curved pipes conveying fluid.Journal of Dynamics and Control,2005,3(1):72~77(in Chinese))
[23] 田耀宗,蹇开林.轴向运动梁的横向振动分析.应用数学和力学,2019,40(10):1081~1088(Tian Y Z,Jian K L.Lateral vibration analysis of axially moving beams.Applied Mathematics and Mechanics,2019,40(10):1081~1088(in Chinese))
[24] 刘涛,罗梦翔,吴炜,等.有限元法的轴向运动梁的激励功率谱辨识.动力学与控制学报,2016,14(2):92~98(Liu T,Luo M X,Wu W,et al.Identification of excitation power spectrum density for an axially moving beam using finite element method.Journal of Dynamics and Control,2016,14(2):92~98(in Chinese))

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输流管道弯曲和振动的有限元分析*

THE FINITE ELEMENT ANALYSIS ON BENDING AND VIBRATION OF THE FLUID-CONVEYING PIPES*

摘要

Abstract

关键词

Keywords

1 物理模型

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

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(19)

2 数值算例

2.1 管道弯曲分析

(20)

2.2 管道自由振动分析

(21)

(22)

(23)

(24)

3 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献

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输流管道弯曲和振动的有限元分析^*

THE FINITE ELEMENT ANALYSIS ON BENDING AND VIBRATION OF THE FLUID-CONVEYING PIPES^*