输流管道系统非线性流固耦合振动研究_熊禾根

[收稿日期]20060325

[作者简介]武汉科技大学 机械传动与制造工程 湖北省重点实验室开放基金项目(2005A13);湖北省教育厅科研资助项目(B200611007)。 [作者简介]熊禾根(1966),男,1987年大学毕业,博士,副教授,现主要从事机械设计与理论、现代设计方法、智能设计制造

执行系统等方面的研究。

输流管道系统非线性流固耦合振动研究

熊禾根,李公法,孔建益杨金堂,蒋国璋,侯 宇,刘怀广 (武汉科技大学机械自动化学院,湖北武汉430081)

[摘要]管道在众多的工业领域中具有十分广泛的应用,发挥着极其重要的作用。围绕输流管道系统的非

线性动力学建模、非线性动力学分析方法和稳定性问题,简述了输流管道系统非线性流固耦合振动的最

新研究情况,并对今后值得进一步研究的某些问题作了分析和预测。

[关键词]输流管道;非线性;流固耦合;稳定性

[中图分类号]U 173;Q327

[文献标识码]A [文章编号]16731409(2006)02057403

输流管道耦合振动具有自激振动的特性,属于非线性动力学研究的重要内容。文献[1,2]的研究表明,输流管道的振动问题的物理模型简明,易于理解、设计和制造。其简单形式的控制方程蕴涵着丰富而复杂的动力学内容,同时也表明对这样问题的非线性动力学研究的必要性。随着数值计算技术、非线性理论与方法研究的不断深入和发展,在输流管道非线性振动方面发现了一些重要现象,主要包括:管道横向挠度引起的轴向拉力对其动力学特性的影响、定常流和振荡流作用下悬臂管的分岔与混沌行为、支承输流管的非线性振动稳定性以及振荡流导致的参数共振。

但是,由于管道流固耦合这一非线性问题的复杂性,还存在一些重要问题需要解决,如寻求更完善的输流管道的动力学建模理论与方法以及探索采用现代非线性动力学分析数值方法研究与揭示其非线性振动机理。笔者将围绕输流管道系统的非线性动力学建模、非线性动力学分析方法、稳定性等3个方面简述输流管道系统非线性流固耦合振动的最新进展情况,同时讨论尚需进一步研究的问题。

1 输流管道非线性动力学建模

由于考虑因素的侧重面不同,建立的管道流固耦合非线性动力学方程也有一定的差别。在实际应用中,管道内径远远小于管道长度,输流直管假设为梁模型是合理有效的。建立动力学方程都假定:流体为无黏不可压;管作为梁模型来处理;管在平面内振动;不计剪切变形和截面转动惯量的影响。

文献[3]采用H am ilton 变分原理导出了两端固支管的非线性动力学模型:

(m +M) u +M V +zM V u +MV u +MV 2u +M V u -EA u -EI (v v +v v )

+(T 0-P -EA )v v -(m +M )g =0(1)

(m +M) v +M V v +2M V v +MV 2v -(T 0-P)v +EI v -EI (3u v +4u v +2u v +v u

+2v 2v +8v v v +2v 3)(T 0-P -EA )(u v +u v +32

v 2v )=0(2)式中,V (t)为流速;E 为管道材料的弹性模量;A 和I 分别为管截面的面积和惯性矩;m 和M 分别为管道和流体的单位长度质量;上标 表示对时间的导数;上标 表示对坐标的导数;g 为重力加速度;u 和v 分别为管轴线的横向位移和轴向位移;T 0为固支管的轴向拉力;P 为其内的流体压力。

文献[4]综合Paidoussis 和Wigg er t 的管道动力学方程,忽略了管道泊松耦合的影响,提出了描述管道非线性流固耦合运动的4-方程模型:

W A p u z -(PA f ) -m f ( V f +V f V f )-mg z -m p u z =0(3) 574 长江大学学报(自科版) 2006年6月第3卷第2期理工卷

Journal of Yangtze University (Nat Sci Edit) Jun 2006,Vo l 3N o 2Sci &Eng V

EI u y +(PA f u y ) +m f ( V f u y +2V f u y +V 2f u y +V f V f u y )+mg y -m u y =0(4)

(PA f ) +m f c 2f (V f -2V f u z )=0

(5)

(PA f ) +m f (g y u y +g z + V f +V f V f +f V f |V f |/(2D))=0

(6)文献[5]在Euler -Bernoulli 梁理论和非线性拉格朗日应变理论的基础上,运用广义哈密顿原理推导出固支管的非线性耦合(横向位移和纵向位移)运动方程:

(m f +m p ) u +m f V (1+u )+2m f V u +m f V 2u -EA (u +32u u +12v v )-32

EIv v =0(7) (m f +m p ) v +m f V v +2m f V v +m f V 2v -12

EA (u v +u v )+EI (v +32u v +3u v +23

u v )=P (8)对该方程用Galerkin 方法进行离散,再在平衡位置领域内对离散了的方程进行线性化,就可以计算出此方程的固有频率。另外,对这些离散化了的非线性方程进行广义 积分(时间)可得出位移随时间变化的轨迹,而且该模型比Paidoussis 的方程更加合理。

文献[6]在利用H amilton 变分原理和描述变形体内流体运动的N -S 方程,建立了描述输流管道非线性流固耦合振动的控制方程,形成描述弱约束管道、输送可压缩流体、具有定常或非定常流动状态系统的非线性4-方程模型。该模型是建立在4个独立变量(轴向位移、横向位移、流速和压力)基础上的全耦合模型,耦合形式包含了摩擦耦合、Poisson 耦合、结合部耦合以及管道轴向和横向运动的耦合。在目前众多的非线性分析模型中,是较为完整的一个模型。

2 非线性流固耦合的非线性动力分析方法研究

输流管是一种用途广泛的工程结构,为了充分认识该系统所蕴涵的丰富的动力学机理,为了全面深入研究流固耦合的管道系统非线性动力学特性,只能依赖于非线性动力分析的现代方法。目前非线性动力学分析使用的主要方法有:中心流形约化方法(center m anifold reduction m ethod);正规化方法(the method of no rmal forms);参数演化方法(the metho d of unfolding param eters);平均化方法(the method o f av er ag ing)以及Ly apunov -Schmidt 约化方法(the method of Lyapuno v -Schm idt reduction)等。中心流形约化方法是为了使原动力系统降维。正规化方法的目的不是降维,而是化简其中的非线性项,减少系数。参数演化方法和前面两个方法不同,它是着重研究系统参数的微小变化对运动特性的影响,这对于弄清参数临界值相应运动的稳定性有重要作用。当状态变量和参数变量的维数都较高时,运动方程的求解难度会大大增加。Lyapunov -Schmidt 约化方法也是一种降维处理技术,它的适用范围较广[1,2,7]。

3 输流管道的动力稳定性研究

文献[8,9]研究了非保守管路系统(两端支承)的稳定性,发现系统除具有一般的叉形分岔失稳外,还可能具有与模态耦合颤振有关的其他失稳形式,称为Paidoussis 后失稳形式。文献[10,11]研究了两端简支的输液管,采用Paido ussis 的管道振动方程无量纲形式,利用Galer kin 离散技术和中心流形理论研究了(二自由度系统)四维空间系统,证实了后失稳存在。进一步研究固支管道在奇点的稳定性时,发现奇点附近可能存在局部分岔,但极限环不存在,运动不稳定。这表明了输流管道系统属于屈曲失稳,输流管不会颤振,也不会出现混沌。其结论可以推广到无穷维系统。

而保守管路系统(悬臂管)稳定性取决于3个参数,即定常流速、管道和流体质量比、流体能量损失系数。当流速较小时(小于分岔临界流速),稳定是渐进的;流速的增加到某一值(临界流速)时系统出现分岔失稳;可以证明在临界流速处满足H opf 分岔条件,并用中心流形方法研究了分岔后周期解的特性[12]。后来,将二维问题扩展到三维问题,研究发现在任何情况下系统均有2个超临界分岔存在,且当流速超过临界值后,运动在平面内分为二枝,随质量比不同,运动可能由驻波通过叉形分岔成为行波,也可能通过鞍点分岔后驻波和行波共存。

575 第3卷第2期熊禾根等:输流管道系统非线性流固耦合振动研究

同时,阻尼对管道系统稳定性的影响也是一个关键因素,在管道参数共振作用下,阻尼虽然不能抑制响应的幅值,但可以改变系统稳定性区域的大小。文献[13,14]以具有粘弹性支承边界约束输流管为对象,研究了材料的各向弹性模量比值、管的细长比、管液质量比和剪切系数等对管道系统稳定性的影响。数值结果表明,这些参数对输流管的稳定性有较大的影响。同时,应用增量平衡法分析具有非线性弹性约束的粘性弹性输流管的振动问题,自由端具有非线性约束的悬臂输流管随着管口参数和流速的变化,系统会有3种失稳形式:静态分岔失稳、H opf 分岔失稳和倍周期分岔失稳。

输流管道非线性动力稳定性研究,以往以考虑流体作用下管道轴向、横向运动耦合非线性为主,即考虑流体运动对系统稳定性的影响,但未考虑管道振动状态的影响,耦合是不完全的。文献[15]以非线性耦合方程为对象,采用模态分解的方式分析了由非定常流引发的悬臂输流管非线性振动的稳定性问题,通过计算得到了前4阶模态运动的相图,悬臂输流管在一定的流速范围内,第一阶模态运动无奇点;第三阶以上模态运动具有相同的稳定性(但临界流速不同),奇点为焦点;第二阶模态运动具有较复杂的运动特性,随流速增加相继出现稳定和不稳定的极限环。

4 结 语

虽然输流管的线性振动研究历史并不短,但非线性振动和运动稳定性的控制却是近几年才起步,不少因素的影响还有待进一步的深入探索。

1)输流管道的非线性动力学建模与分析方法。复杂输流管的壳体系统的非线性动力有限元模型的研究是一个方向,其中研究内容应该包括多种流固耦合的因素,如壳壁附近流体粘性造成的影响,轴流和环境同时作用的影响,材料阻尼等因素的影响等。程序应该具有更广泛的通用性,易操作性。

2)力求从解决高维系统和提高计算精度两个方面去进一步寻求更有效的非线形动力学等分析方法。

3)随机激励下管道振动及分析方法。振荡流是一种扰动,它的变化带有随机性,因此将振荡流引起输流管道的振动看成是一个非线形随机激励系统,用概率统计的方法加以研究这类系统的随机分叉将更有现实意义。

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[编辑] 洪云飞

576 长江大学学报(自科版)2006年6月

Vo l 3N o 2MAIN ABSTR AC TS

WU Zhao-fu (Jing zh ou I nstitute of T ech nolog y,J ing z hou434100)

Abstract:The paper studies cur rent P2P netw ork w ith pow er law and small w orld pr operty Based o n it,dev ise a architecture for the P2P netw ork,m ake sev eral mo difications to the existed proto-cols This P2P netw ork has less average shor test path leng th with better scalability and robustness Key words:small w orld property;P2P netw ork;average shortest path length

550Facial Feature Recognition Based Immu nity Algorithm and Support Vector Machine ZHOU Tian-ho ng (Yu nyang T eache rs College,Danj iang kou442700;W uhan Univ er sity,Wu han430072)

ZHANG Jiang-qing (Wu han Univ ersity,W uhan430072)

CAO Da-yo u (Yunyang Teac her s Colleg e,Danj iangkou442700)

Abstract:A m ethod for facial feature recog nition based on im munity algo rithm and suppo rt vector m achine is pro posed Because the learning suppor t v ector machine is an instructing learning,a nega-tive alg orithm is introduced T he negativ e result of facial feature is pro vided for the support vector m achine learning The co mplex ity of o peratio n is g reatly reduced T he result show s that com pared w ith other m ethod,the m ethod has a hig h reco gnition r ate

Key words:facial feature recognitio n;im munity algor ithm;support vector machine

556Simply Polygon Triangulation Algorithm Based on Minimum Distance

CAO Qing-long,LI Jun (Yang tz e Univ er sity,J ing z hou434023)

Abstract:The triangulation algor ithm based on minimum distance is a cor respo nding distance o f each apex of the po lyg on The distances are contrasted and based on the continuous m inimum dis-tance in turn After that,judging neighbo ring tw o apex rug ged topog raphy and chang ing the dis-tance of the junction point s consecutive point Except the concaving po int,it isn t necessary to judg e and calculate all points Therefor e,the result of triang ulation confor ms to the requirement completely;w hat s m ore,the style of net is somew hat good and co nform s to the empty circle principle basically

Key words:tr iangulatio n;poly go n;alg orithm

566Operational Management and Resource Scheduling for campus Grid

ZHANG Ya n-he,CH EN Zhong (Yangtz e Univ er sity,Jing zh ou434023)

Abstract:Cam pus grid is used fo r sharing the com putational resources in the campus netw orks for r educing cost to enhance the usage of the co mputational reso urces T he m anagement Softw are Sun Grid Engine(SGE)is intro duced into the gr id,the introduction o f SGE-supported computational r esources is w idely expanded T he scheduling stratig y o f itself is used to manag e the local r esources in the resour ce lev el It is combined w ith Glo bus T oolkit to integ rate the g rid level w ith resource lev-el closely in the campus grid After the job is submitted,SGE oper ation state info rmation is accu-rately reflected in the g rid level in rea-l time,by w hich the co mputatio nal resources ar e transparent to the user s in campus g rid

Key words:campus g rid;resource scheduling;Globus Too lkit;Sun Grid Eng ine

574Research on Nonlinear FSI Vibration of Fluid Conveying Pipes

XIONG He-g en,LI Gong-fa,KONG Jian-y i,YANG Jin-ta ng,JIANG Guo-zhang,H O U Yu,LIU H ua i-gua ng (W uhan Univ er sity of S cience and T ec hnology,W uhan430081)

Jo u rna l o f Ya n gtze Un ive rsity(N atu ral Scie n ce Editio n)N o 2 2006

Abstract:Pipes are w idely used in industry and play a quite important ro le So me recent research de-velopment on nonlinear FSI v ibration of fluid conveying pipes is review ed in this paper It fo cuses o n nonlinear dynamic m odeling theories,mo dern analy tical methods for so lving these dynam ic prob-lems and stability of fluid conveying pipes Finally the future trends and adv ances in this ar ea are dis-cussed

Key words:fluid conveying pipes;nonlinear;FSI;stability

577Research on Vibration Characteristics of Fluid-filled Pipelines

ZENG Guo-hua,KONG Jian-y i,LI Go ng-fa,YANG Jin-ta ng,XIONG H e-ge n,JIANG Guo-zha ng (W uhan Univ er sity of S cience and T ec hnology,W uhan430081)

Abstract:There are bro ad applications for the research on v ibration characteristics of fluid-filled pipeline fluid,w hich has very important function for the prog ress o f basic science theor ies and the developm ent of national economy,fluid-structure interaction,the resear ch on vibr ation characteris-tics in fluid-filled pipelines are studied,research methods and their application sco pe are ana-ly zed T hen the typical models of fluid-filled pipelines studied are explored These hav e certain refer-ence value w ith further research in the future

Key words:fluid-filled pipeline;vibratio n character istics;fluid-structure interaction;m odel

579Design of Control S ystem for Potable Oil Pipe Mark Printer Based on Micro-computer LI Kun-quan,ZHAI Qun-fang (Yang tz e Univ er sity,Jing z hou434023)

Abstract:A pneumatic m ark pr inter based o n m icro-com uter is discussed T he overall desig n o f the printer system and the implem entation of the contr ol sy stem are introduced in detail T he m odulus for inform ation input and the implementatio n of cor respo nding m otion are introduced em phatically, the open and close of soleno id valve are co ntro lled by pulse to co ntro l the printing pin Its cost is re-duced through the development of hardw are cir cuit,by w hich the vo lum e of printer is reduced and its stability is impr oved

Key words:micro-computer;step m otor;hardw are system;m ark printer

591Detection of Single-pile Vertical Bearing C apacity with Steady Mechanic Impedance Method

MAO Bin (S henz he n East Constr uction S up er v ision Co ,S hen zhe n518034)

LUO Rui-ping (Yang tz e Univ er sity,J ing z hou434023)

Abstract:T he pile-soil m odel is simplified to mass-spr ing elastic system w hich is under mechanical impedance fo rce impulse T he key for load-bearing capacity calculation is accurat for dynam ic stiff-ness testing When the calculatio n is m ade,accur ate calculating fo rmulae should be used for obta-i ning rapid and m ore accur ate results on the basis of testing data

Key words:static stiffness;dynamic rig idity;m echanical impedance m ethod;vertical bearing ca-pacity;limit settlement value

Translated&Edited by SU Ka-i ke(苏开科)