Recent advances in research on large-defomation dynamics of slender pipes conveying fluid
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摘要: 细长输流管道是发动机液压装置、航空加油机、核工业热交换器、海洋钻井平台等工程装备系统的一类重要结构. 当流速较高时, 细长管道可能会发生屈曲或颤振等流致失稳现象, 严重时可酿成重大安全事故. 输流管道的流致失稳及其非线性振动是典型的流固耦合力学行为, 已成为结构动力学、流固耦合力学等研究领域的一个普遍性范例. 在建立动力学方程、明确稳定性机理和分析非线性振动规律之后, 近年来人们极其关注输流管道的大变形/大位移动力学问题. 本文系统介绍了细长输流管道非线性振动, 特别是其弯曲大变形动力学的研究进展. 首先, 概述了输流管系统的非线性特征及其分类, 简要分析了一些常用假设的合理性. 其次, 重点介绍了泰勒展开近似模型、几何精确理论模型、绝对节点坐标描述计算模型、数据驱动模型及相关的其他建模与求解方法. 然后, 针对两端支撑管道和悬臂管道两类有本质区别的动力学系统, 回顾了其非线性动力学机理与演化规律, 重点介绍了悬臂管道从小变形假设到大变形响应的一些新近研究进展. 在此基础上, 还介绍了提高输流管稳定性、抑制输流管非线性振动和利用输流管大变形响应的主要方法. 最后, 对细长输流管道大变形动力学的研究现状进行了归纳总结, 并指出值得关注的几个基础性科学问题.Abstract: Slender pipes conveying fluid are an important structure in various engineering equipment systems such as engine hydraulic device, aviation tanker, nuclear heat exchanger and offshore drilling platform. When the flow velocity is sufficiently high, the slender pipe may be subjected to flow-induced instability including buckling and flutter, which may lead to safety accidents in serious cases. Flow-induced instability and nonlinear vibration of pipes conveying fluid are typical fluid-structure interaction behaviors, and have become a generic paradigm and fertile dynamics problem in nonlinear dynamics and fluid-structure interaction mechanics. After establishing governing equation, clarifying the stability mechanism and analyzing the nonlinear vibration mechanism of pipes conveying fluid, much attention has been payed to the large-deformation dynamics of this dynamical system in recent years. In this review, the research progress of nonlinear vibrations, especially the large-deformation bending dynamics of slender pipes are systematically introduced. Firstly, the nonlinear characteristics and classification of the fluid-conveying pipe system are summarized, and the applicability of some common assumptions is briefly analyzed. Secondly, the Taylor expansion approximation model, Geometrically exact model, Absolute node coordinate formulation model, Data-driven model and other related modeling and solving methods were reviewed. Then, the nonlinear dynamics mechanism and evolution law of cantilevered and supported pipes are reviewed, and some recent research progress of cantilevered pipes from small-deformation hypothesis to large-deformation response is emphasized. On this basis, several typical methods of improving the stability of the pipe, suppressing the nonlinear vibrations of the pipe and utilizing the large-deformation response of the pipe are also introduced. Finally, the research status of large-deformation dynamics of slender pipe conveying fluid is summarized, and several basic scientific problems worthy of attention are pointed out.
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图 1 输流管道在工程技术领域的典型应用: (a)海洋输流管道, (b)航空加油管, (c)发动机燃料管路, (d) 水下仿生水母 (a、b、c图来源于网络, d图源于何毅翔等 2024)
图 4 管道中线的(a)三维和(b)二维精确几何关系示意图(Chen et al. 2021)
图 5 输流曲管在绝对节点坐标下变形前后的微元几何关系(Zhou et al. 2021)
图 6 RBFNN结构示意图(Xu et al. 2023a)
图 7 FF-PINN的网络传递框架示意图(Zhang et al. 2024)
图 8 基于谱子流形(SSM)的输流管道数据驱动模型降阶流程图(Li et al. 2024)
图 10 轴向刚度参数Π0、重力参数γ和张力参数Г对两端支撑输流管道分岔图的影响 (Modarres-Sadeghi & Païdoussis 2009)
图 11 半个正弦波初始构型输流曲管的前四阶无量纲频率随无量纲流速的演化曲线: (a) 未考虑静变形, (b) 考虑静变形(Zhou et al. 2021)
图 12 不同圆弧角曲管的静位移随流速变化的分岔图与静变形构型: (a) 圆弧角为0° (直管), (b)圆弧角为0.01°, (c) 圆弧角为1°, (d) 圆弧角为10°, (e) 圆弧角为19°, (f) 圆弧角为60° (Yan et al. 2023)
图 13 内流速U0=2 m/s时三维螺旋管的振动形状: (a)数值仿真结果, (b)实验测试结果(Łuczko & Czerwinski 2022)
图 14 三维输流曲管示意图和一些典型计算结果: (a) 螺旋输流曲管示意图和u = 0时的前两阶模态形状, (b)直-弯空间管道示意图和u = 0时的前两阶模态形状(Guo et al. 2024a)
图 15 悬臂输流管道的二阶模态颤振失稳: (a) 悬臂输流管系统模型图; (b) 复特征频率的Argand图(Gregory & Païdoussis 1966)
图 16 侧向弹簧支撑作用下的悬臂输流管道: (a) 模型示意图; (b) 弹簧支撑位于管道末端时的管道屈曲构型; (c) 弹簧支撑位于0.75L (L为管长) 处时管道的静态屈曲构型; (d) 弹簧支撑位于0.5L处时管道的颤振失稳形态(Sugiyama et al. 1985)
图 17 悬臂输流直管模型示意图及其临界流速演化规律: (a) 悬臂输流直管的空间振动模型示意图; (b) 端部含集中质量管道系统的临界流速随质量比参数的演化曲线 (Modarres-Sadeghi et al. 2007)
图 18 单点弹簧约束作用下输流直管的动态响应: (a) 流速为6.7, (b) 流速为9.1, (c) 流速为9.3和(d) 流速为10.1时的频谱分析实验结果 (Ghayesh & Païdoussis 2010)
图 19 单点环形碰撞约束下的悬臂输流直管: (a) 管道与碰撞模型示意图; (b) 圆形碰撞约束剖面图 (Wang et al. 2018)
图 20 几何精确模型和泰勒展开模型预测的悬臂管道自由端的动态响应结果对比: (a) 悬臂直管模型示意图, (b) 基于几何精确模型预测的管道时域响应和 (c) 相轨迹图; (d) 基于泰勒展开模型预测的管道时域响应和 (e) 相轨迹图 (Chen et al. 2019)
图 21 质量比为0.2时悬臂输流直管动态响应的几何精确理论模型预测结果: (a) 无量纲流速为9时的管道三维振动形态; (b) 无量纲流速为10时的管道三维振动形态; (c)无量纲流速为12时管道二维振动形态及其俯视图 (Chen et al. 2021)
图 22 含末端质量块的输流直管系统: (a) 管道模型示意图, (b) 无量纲流速u = 7.42、u = 8.83和u = 10.00时的管道振动形态图 (Farokhi et al. 2021)
图 23 含有局部刚性段的悬臂输流直管系统 (红色线条为刚性段): (a) 管道模型示意图; (b)和(c) 刚性段在不同位置时管道的振动形态图 (Zhou et al. 2020)
图 24 站立式悬臂输流管道在重力参数γ= −50时的大变形动力学响应: (a) 管道自由端位置随流速变化的分叉图; (b)和(c) ANCF模型预测与实验测试结果对比图. (a)和(b)中的黑粗线和蓝细线分别为管道构型的实验测试结果与ANCF计算结果 (Chen et al. 2024)
图 25 四种初始构型的微弯悬臂管在高流速下的颤振响应行为: (a) 四种微弯曲管的模型示意图; (b) 四种微弯曲管在高流速下的振动形态图(Zhou et al. 2021)
图 26 L形悬臂曲管在定常内流作用下的静态和动态响应: (a) L形输流曲管模型示意图; (b) L形曲管自由端沿X方向位移在不同流速下的分岔图 (Zhou et al. 2022)
图 27 内流作用下顶端张紧曲管的动力学行为: (a)曲管系统示意图; (b) 不同时刻的管道振动形态图 (Tang & Sweetman 2021)
图 28 半圆形悬臂曲管在内流作用下的几何精确动力学模型及其计算结果: (a)半圆形悬臂曲管变形前后的几何描述示意图; (b)流速略高于临界流速值 (v = 5) 时管道的管道静平衡位置 (红色线条) 和振动形态 (蓝色线条) 图; (c)流速远高于临界流速值 (v = 8.5) 时的管道静平衡位置和振动形态图 (Chen et al. 2022)
图 29 Misra等人模型和几何精确理论模型预测的半圆形曲管复特征频率: (a) Misra等人模型预测的颤振临界流速约为2.2 (Misra et al., 1988); (b)Chen等人基于几何精确理论模型预测的颤振临界流速约为9.2 (Chen et al. 2022)
图 30 不同质量比β参数取值下半圆形悬臂曲管的复特征频率: (a) β=0.2时系统发生二阶模态失稳的Argand图; (b) β=0.5时系统发生三阶模态失稳的Argand图; (c) β=0.9时系统发生二阶模态失稳的Argand图 (Cao et al. 2024)
图 31 锥形螺旋线初始构型下悬臂输流曲管的三阶、五阶、六阶模态分析结果: (a) 流速为0的情形; (b) 无量纲流速为6的情形 (Łuczko & Czerwiński 2019)
图 32 基础激励下悬臂微弯曲管自由端的准周期运动: (a)位移时间历程曲线, (b)振动相轨迹图, (c) 振动形态图(Zhu et al. 2023)
图 33 直-弯组合悬臂平面曲管的稳定性与动态响应: (a)直-弯组合平面曲管模型示意图; (b) 曲管在面内 (蓝线) 和面外 (红线) 的复特征值曲线; (c) 流速略高于临界值时管道的三维振动形态图及其在Y-Z和X-Y平面的投影; (d) 悬臂曲管末端位移在X方向、Y方向和Z方向上的相轨迹曲线 (Guo et al. 2024b)
图 34 杠杆型非线性能量阱在输流管道被动控制中的应用示意图(Cao et al. 2022)
图 35 几种典型的非线性隔振器: (a) NES胞元示意图 (Ding & Shao 2022); (b) NES隔振器 (Ding & Chen 2020); (c)二维逆变器增强型隔振器 (Yang et al. 2024); (d)杠杆型非线性隔振器 (Zang et al. 2021)
图 36 非线性准零刚度隔振器在两端弹性支撑输流管道系统中的应用示意图 (Ding et al. 2019)
图 37 外磁场作用下的硬磁软材料悬臂输流管道: (a)模型示意图; (b) 不同磁场方向角度下管道失稳临界流速随外部磁场强度的演化曲线 (Chen et al. 2021)
图 38 局部磁化悬臂输流管道的静变形和周期振动响应: (a)磁化和未磁化输流管道端部位移时程曲线对比图; (b) 磁化后输流管道端部相轨迹曲线, (c) 振动形态图 和 (d) 庞加莱映射图 (Guo et al. 2022)
图 39 一种协同推进的仿生鱼设计方案 (Strefling et al. 2012)
图 40 一种基于输流管大变形的仿生机器人设计方案: (a) 实验测试照片; (b) CFD仿真计算得到的尾涡脱落云图 (Dai et al. 2022)
图 41 用于微创生物打印的铁磁软导管机器人 (FSCR) 系统: (a) 通过小切口在体内使用功能墨水 (如导电聚合物和生物材料) 进行微创打印的示意图; (b) 使用带有大切口的刚性喷嘴的传统打印系统示意图 (Zhou et al. 2021)
图 42 附有非线性能量阱和能量采集器的两端支撑输流管道: (a) 输流管道系统模型示意图; (b) 能量采集率和阻尼耗散率随流速的变化曲线 (Jin & Yang 2023)
表 1 输流管动力学数据驱动建模的三种方法及其特征对比
作者 方法 主要特征 Xu et al. 2023a, b RBFNN 应用POD降阶处理, 再进行RBFNN建模预测 Zhang et al. 2024 FF-PINN 应用傅里叶特征映射处理数据以改良PINN模型 Li et al. 2024 SSM 应用SSM降阶模型并合理外推预测复杂非线性动力学行为 
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