大跨度悬索桥成桥状态颤振分析
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摘要
颤振是一种发散性的自激振动,它的发生主要是由于振动的结构能够在流动的空气中不断吸收能量,而该能量又大于结构阻尼在振动中所耗散的能量而引起的。当今,随着悬索桥跨度的日益增大,其刚度和阻尼显著减小,因此悬索桥的颤振稳定性已经成为大跨度悬索桥设计和施工中的关键问题。
本文以主跨为1418m的南京四桥为工程背景,在现有的颤振频域和时域分析方法的基础上,通过计算分析和风洞试验,对大跨度悬索桥颤振问题进行了研究。
本论文的主要工作有以下几方面：
首先回顾了颤振的分析理论,然后基于桥梁二维颤振和三维多模态耦合颤振分析理论,运用数值编程软件编制了桥梁二维和三维颤振分析程序,并通过一个典型算例验证了程序的正确性和可靠性,之后对南京四桥成桥状态进行二维和三维颤振频域分析。
其二,讨论了桥梁结构上的气动自激力在时域中的处理问题：利用有限元理论,把自激力的作用等效为作用在结构上的附加气动刚度矩阵和气动阻尼矩阵,实现自激力的时域化。基于有限元软件实现了桥梁颤振的时域分析,并通过一个典型算例验证了此方法的正确性和可靠性,然后结合南京四桥,对其进行成桥状态的三维颤振时域分析。
其三,以南京四桥为工程背景,详细介绍在风洞中进行桥梁颤振试验的方法,研究该桥颤振特性并得出试验颤振临界风速,同时利用Van der Put颤振估算公式进行颤振临界风速的近似计算。继而通过采用平板颤振导数和实桥颤振导数,利用频域和时域分析方法,研究了桥梁颤振临界风速随结构阻尼比和来流风攻角变化的一般规律,探讨了颤振导数对桥梁颤振稳定性的影响,得到了一些有意义的结论。
Flutter is a kind of divergent self-excited vibration, it occurs because the vibrating structure can absorb energy continuously from the airflow, that is greater than the energy consumed by the structural damping. Today, spans of suspension bridges becoming longer and longer, the stiffness and the damping of structures decrease obviously, so the flutter stability has become a very important aspect in the design and construction of long-span suspension bridges.
In this thesis, by taking the 4th nanjing suspension bridge over Yangtze river with the main span of 1418m as an example, based on the existing frequency-domain flutter analysis and time-domain flutter analysis, flutter instability of the long-span suspension bridge is studied by theory analysis and wind-tunnel test.
The main work of this thesis as follows:
First of all, the flutter analysis theory is reviewed. Based on the 2D flutter analysis method and 3D multi-mode flutter analysis method of the bridge, the flutter analysis program is compiled using numerical programming software. One classic example is taken to prove the two programs's correctness and validity. Then the flutter stability of the completion stage is analyzed in frequency-domain.
Secondly, how to express the self-excited aerodynamic force in time-domain is discussed. Based on the finite element formulation, the self-excited aerodynamic force has been considered as equivalent aerodynamic stiffness matrix and equivalent aerodynamic damping matrix in order to express the self-excited aerodynamic force in time-domain. A program is developed using the finite element software for 3D flutter analysis in time-domain, and one classic example is taken to prove the program's correctness and validity. Then combined with the the 4th nanjing suspension bridge, analyzing its flutter stability in time-domain.
Thirdly, with the 4th nanjing suspension bridge as background, introduce the flutter test of the bridge in wind tunnel and study the flutter characteristic of the girder and determine it's critical wind speed of flutter. At the same time, this thesis uses the formula of Van der Put to estimate the critical wind speed of flutter. Furthermore, the general rules of the flutter stability influenced by the different wind attack angle and structural damping are discussed with flutter derivatives of plate and actual girder using frequency-domain flutter analysis and time-domain flutter analysis. Then the influence is also studied of the flutter derivatives on the the flutter stability of the bridge. At the end, This thesis analyzes the causes and some useful conclusions are drawn.
本文以主跨为1418m的南京四桥为工程背景,在现有的颤振频域和时域分析方法的基础上,通过计算分析和风洞试验,对大跨度悬索桥颤振问题进行了研究。
本论文的主要工作有以下几方面：
首先回顾了颤振的分析理论,然后基于桥梁二维颤振和三维多模态耦合颤振分析理论,运用数值编程软件编制了桥梁二维和三维颤振分析程序,并通过一个典型算例验证了程序的正确性和可靠性,之后对南京四桥成桥状态进行二维和三维颤振频域分析。
其二,讨论了桥梁结构上的气动自激力在时域中的处理问题：利用有限元理论,把自激力的作用等效为作用在结构上的附加气动刚度矩阵和气动阻尼矩阵,实现自激力的时域化。基于有限元软件实现了桥梁颤振的时域分析,并通过一个典型算例验证了此方法的正确性和可靠性,然后结合南京四桥,对其进行成桥状态的三维颤振时域分析。
其三,以南京四桥为工程背景,详细介绍在风洞中进行桥梁颤振试验的方法,研究该桥颤振特性并得出试验颤振临界风速,同时利用Van der Put颤振估算公式进行颤振临界风速的近似计算。继而通过采用平板颤振导数和实桥颤振导数,利用频域和时域分析方法,研究了桥梁颤振临界风速随结构阻尼比和来流风攻角变化的一般规律,探讨了颤振导数对桥梁颤振稳定性的影响,得到了一些有意义的结论。
Flutter is a kind of divergent self-excited vibration, it occurs because the vibrating structure can absorb energy continuously from the airflow, that is greater than the energy consumed by the structural damping. Today, spans of suspension bridges becoming longer and longer, the stiffness and the damping of structures decrease obviously, so the flutter stability has become a very important aspect in the design and construction of long-span suspension bridges.
In this thesis, by taking the 4th nanjing suspension bridge over Yangtze river with the main span of 1418m as an example, based on the existing frequency-domain flutter analysis and time-domain flutter analysis, flutter instability of the long-span suspension bridge is studied by theory analysis and wind-tunnel test.
The main work of this thesis as follows:
First of all, the flutter analysis theory is reviewed. Based on the 2D flutter analysis method and 3D multi-mode flutter analysis method of the bridge, the flutter analysis program is compiled using numerical programming software. One classic example is taken to prove the two programs's correctness and validity. Then the flutter stability of the completion stage is analyzed in frequency-domain.
Secondly, how to express the self-excited aerodynamic force in time-domain is discussed. Based on the finite element formulation, the self-excited aerodynamic force has been considered as equivalent aerodynamic stiffness matrix and equivalent aerodynamic damping matrix in order to express the self-excited aerodynamic force in time-domain. A program is developed using the finite element software for 3D flutter analysis in time-domain, and one classic example is taken to prove the program's correctness and validity. Then combined with the the 4th nanjing suspension bridge, analyzing its flutter stability in time-domain.
Thirdly, with the 4th nanjing suspension bridge as background, introduce the flutter test of the bridge in wind tunnel and study the flutter characteristic of the girder and determine it's critical wind speed of flutter. At the same time, this thesis uses the formula of Van der Put to estimate the critical wind speed of flutter. Furthermore, the general rules of the flutter stability influenced by the different wind attack angle and structural damping are discussed with flutter derivatives of plate and actual girder using frequency-domain flutter analysis and time-domain flutter analysis. Then the influence is also studied of the flutter derivatives on the the flutter stability of the bridge. At the end, This thesis analyzes the causes and some useful conclusions are drawn.
引文
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[2]严国敏.现代悬索桥[M].北京：人民交通出版社,2002
[3]李亚东.桥梁工程概论[M].成都：西南交通大学出版社,2006
[4]廖海黎,奚绍中.改善大跨度桥梁抗风稳定性的建议[J].国外桥梁,1999
[5]周昌栋,谭永高,宋官保.悬索桥上部结构施工[M].北京：人民交通出版社,2004
[6]雷俊卿,郑明珠,徐恭义.悬索桥设计[M].北京：人民交通出版社,2002
[7]张相庭.结构风压和风振计算[M].同济大学出版社,1985
[8]公路桥梁抗风设计规范(JTG/G D60-01-2004) [S].北京：人民交通出版社,2004
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[10]周述华.大跨度悬索桥空间非线性抖振响应仿真分析[D].成都：西南交通大学博士学位论文.1993
[11]李永乐.风-车-桥系统非线性空间耦合振动研究[D].成都：西南交通大学博士学位论文.2003
[12]陈政清.桥梁风工程[M].北京：人民交通出版社,2005
[13]曹映泓.大跨度桥梁非线性颤振和抖振时程分析[D].上海：同济大学博士学位论文.1999
[14]丁泉顺.大跨度桥梁耦合颤抖振响应分析[D].上海：同济大学博士学位论文.2006
[15]DavenPort A.G The application of statistical concepts to the wind loading of structur-es.Proc.ICE,1961,19(2)
[16]Scanlan R.H.,Tomko,J.J.Aiufoil and bridge deck flutter derivatives J. Engrg . Mech.Div, ASCE.1971,97(ST6)
[17]Davenport A.G Buffeting of a suspension bridge by storm winds. J. structural Division, ASCE.1962,88 (ST3):233-268
[18]Scanlan,R.,J.Beliveau,and K.Budlong, Indicial aerodynamic functions for bridge decks.Journal of the Engineering Mechanics Division,1974.100(4):p.657-672
[19]Bucher,C. and Y.Lin,Effect of spanwise correlation of turbulence field on the motion stability of long-span bridges. Journal of Fluids and Structures,1998.2(5):p.437-451
[20]Agar,T.,Aerodynamic flutter analysis of suspension bridges by a modal technique. Engine-ering Structures,1989.11(2):p.75-82
[21]胡晓伦.大跨度斜拉桥颤抖振响应及静风稳定性分析[D].上海：同济大学博士学位论文.2006
[22]王新敏.ANSYS工程结构数值分析[M].北京：人民交通出版社,2007
[23]埃米尔·希缭,罗伯特·H·斯坎伦.风对结构的作用—风工程导论[M].刘尚培、项海帆等译.同济大学出版社,1992
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