钢梁斜拉桥车桥耦合振动分析
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摘要
车辆荷载作用下,桥梁的动力响应一直是桥梁工程界里的研究热点,因为这关系到桥梁在营运阶段的使用安全性及舒适性,尤其对于钢桥而言,车致振动还能引起结构的疲劳损坏,故车桥耦合振动的研究在评价桥梁动力安全性能方面也就具有了很大的现实意义和工程应用价值。
在阅读了大量文献的基础上,本文作者回顾了国内外学界在这一领域的研究成果并基于此做了较详细的总结。
本文前四个章重点对流行的车桥耦合振动分析理论进行了介绍。首先是给出了斜拉桥结构动力有限元分析的理论基础和数学表达,并介绍了经典的结构动力分析理论,阐述了如何进行结构的频率和模态分析。
接着推导了车辆的振动分析模型,并分别详细给出了三维,二维车辆模型的显示振动方程。在此基础上,结合桥面平整度的概念,推导了车桥耦合振动机理,即二者间的联系:几何协调和作用力协调并完整地给出了数学表达。随后专门针对桥面平整度的数值模拟给出了理论模型和实例计算。在求解车桥耦合振动方程上,本文分别推导了模态综合法和迭代法的数学表达。
最后结合工程实例,分析了沈阳蒲河尚小桥在几种单车影响因素作用下的车桥耦合振动响应。得出了车速,车辆加速度及车重同尚小桥动力响应间的关系。结论可供该课题进一步研究作理论参考和数据借鉴。
It has always been a popular research point to investigate the dynamics of bridges induced by interaction of vibration between bridge and vehicle, because it has huge connections with the service ability of the bridges investigated. Especially for steel bridges, vehicle induced vibration can cause serious fatigue of the bridges that could lead to damage and failure. Thus, it has huge implications in practical bridge engineering regarding evaluating of the service safety of bridges to research the interaction between vehicle and bridge vibration.
On the basis of sufficient literature review, the author made a detailed summary of the related former works achieved abroad and home.
In the first four chapters introduced are the current analysis theories regarding this topic. At first theory basis and mathematical formulations are given with respect to dynamic analysis of cable-stayed bridges. Besides classical dynamical analysis theories are addressed and in particular stated is how to carry out modal analysis of structures.
Secondly, vibration equation of the vehicle is derived and three unique types of equations of the vehicle mode ls including 3D and 2D models are also given explicitly. Then combined with pavement roughness profile, the connections between vehicle and bridge vibration are addressed by displacement compatibility condition and force equilibrium. As for numerical simulation of pavement roughness profile, it is also addressed here in the paper. In the end two ways of solving the coupling vibration equation are introduced by their mathematical formulations, which are component mode synthesis method and separation iteration method.
Finally, one practical bridge, the Puhe River Shangxiao Bridge in Shenyang, is investigated when under single truck travelling along its span. Relationships are developed between the dynamical response of the bridge and parameters of the single moving truck which are vehicle velocity, vehicle acceleration and vehicle weight. Conclusions derived here in this thesis can be referred by further study in the area and also provide certain perspectives toward the bridge’s practical engineering problems.
在阅读了大量文献的基础上,本文作者回顾了国内外学界在这一领域的研究成果并基于此做了较详细的总结。
本文前四个章重点对流行的车桥耦合振动分析理论进行了介绍。首先是给出了斜拉桥结构动力有限元分析的理论基础和数学表达,并介绍了经典的结构动力分析理论,阐述了如何进行结构的频率和模态分析。
接着推导了车辆的振动分析模型,并分别详细给出了三维,二维车辆模型的显示振动方程。在此基础上,结合桥面平整度的概念,推导了车桥耦合振动机理,即二者间的联系:几何协调和作用力协调并完整地给出了数学表达。随后专门针对桥面平整度的数值模拟给出了理论模型和实例计算。在求解车桥耦合振动方程上,本文分别推导了模态综合法和迭代法的数学表达。
最后结合工程实例,分析了沈阳蒲河尚小桥在几种单车影响因素作用下的车桥耦合振动响应。得出了车速,车辆加速度及车重同尚小桥动力响应间的关系。结论可供该课题进一步研究作理论参考和数据借鉴。
It has always been a popular research point to investigate the dynamics of bridges induced by interaction of vibration between bridge and vehicle, because it has huge connections with the service ability of the bridges investigated. Especially for steel bridges, vehicle induced vibration can cause serious fatigue of the bridges that could lead to damage and failure. Thus, it has huge implications in practical bridge engineering regarding evaluating of the service safety of bridges to research the interaction between vehicle and bridge vibration.
On the basis of sufficient literature review, the author made a detailed summary of the related former works achieved abroad and home.
In the first four chapters introduced are the current analysis theories regarding this topic. At first theory basis and mathematical formulations are given with respect to dynamic analysis of cable-stayed bridges. Besides classical dynamical analysis theories are addressed and in particular stated is how to carry out modal analysis of structures.
Secondly, vibration equation of the vehicle is derived and three unique types of equations of the vehicle mode ls including 3D and 2D models are also given explicitly. Then combined with pavement roughness profile, the connections between vehicle and bridge vibration are addressed by displacement compatibility condition and force equilibrium. As for numerical simulation of pavement roughness profile, it is also addressed here in the paper. In the end two ways of solving the coupling vibration equation are introduced by their mathematical formulations, which are component mode synthesis method and separation iteration method.
Finally, one practical bridge, the Puhe River Shangxiao Bridge in Shenyang, is investigated when under single truck travelling along its span. Relationships are developed between the dynamical response of the bridge and parameters of the single moving truck which are vehicle velocity, vehicle acceleration and vehicle weight. Conclusions derived here in this thesis can be referred by further study in the area and also provide certain perspectives toward the bridge’s practical engineering problems.
引文
1刘士林.斜拉桥.北京,人民交通出版社, 2002: 1~6
2 R. Cal?ada, A. Cunha, R. Delgado. Analysis of traffic-induced vibration in a cable-stayed bridge. Part I: Experimental assessment. Journal of Bridge Engineering. 2005, 10(4): 370~385
3 R. Cal?ada, A. Cunha, R. Delgado. Analysis of traffic-induced vibration in a cable-stayed bridge. Part II: Numerical modeling and stochastic simulation. Journal of Bridge Engineering. 2005, 10(4): 386~397
4 X. Shi, C. S. Cai. Vehicle induced dynamic behavior of short-span slab bridges considering effect of approach slab condition. J Bridge Engineering. 2008, 13(1): 83~92
5 H. H. Jeffcott. On the vibration of beams under the action of moving loads. Philosophical Mag. 1929, 8(48): 66~97
6 C. P. Tan. Dynamic response of a horizontally curved bridge. Journal of Struct Div. 1968a, 94(3): 761~781
7 C. P. Tan. Response of a horizontally curved bridge to moving loads. Journal of Struct Div. 1968b, 94(9): 2135~2151
8 S. Timoshenko. Vibration problems in engineering. 4th Ed. New York: Wiley, 1974: 1~10
9 G. B. Warburton. The dynamical behavior of structures. 2nd Ed. England, Oxford: Pergamon Press, 1976: 1~20
10 N. Sridharan. Numerical analysis of vibration of beams subjected to moving loads. J Sound & Vibration. 1979, 65(1): 147~150
11 T. E. Blejwas. Dynamic interaction of moving vehicles and structures. J Sound & Vibration. 1979, 67(4): 513~521
12 M. J. Inbanathan. Bridge vibrations due to vehicle moving over rough surface. J Struct Engrg. 1987, 113(9): 1994~2008
13 J. E. Akin. Numerical solution for response of beams with moving mass. J StructEngrg. 1989, 115(1): 120~131
14林海,肖盛燮.桥梁车辆振动分析理论评述.重庆交通学院学报. 1998, 17(3): 1~9
15 E. S. Hwang, A. S. Nowak. Simulation of dynamic load for bridges. J Struct Engrg. 1991, 117(5): 1413~1434
16 Ton-Lo Wang, Dongzhou Huang. Cable-stayed bridge vibration due to road surface roughness. J Struct Engrg. 1992, 118(5): 1354~1374
17 Yeong-Bin Yang, B. H. Lin. Vehicle-bridge interaction analysis by dynamic condensation method. J Struct Engrg. 1995, 121(11): 1636~1643
18 Yeong-Bin Yang, Jong-Dar Yao. Vehicle-bridge interaction element for dynamic analysis. J Struct Engrg. 1997, 123(11): 1512~1518
19 G. H. Tan, G. H. Brameld. Development of an analytical model for treating bridge-vehicle interaction. Engineering Structures. 1998, 20(1-2): 54~61
20谭国辉.车辆与桥梁相互作用的系统模拟.土木工程学报. 1996, 29(3): 34~41
21 Y. L. Xu, W. H. Guo. Dynamic analysis of coupled road vehicle and cable-stayed bridge systems under turbulent wind. Engineering Structures. 2003, 23: 473~486
22 L. Kwasniewski, Hongyi Li, Jerry Wekezer, et al. Finite element analysis of vehicle-bridge interaction. Finite Element in Analysis and Design. 2006, 42: 950~959
23毛清华.移动车辆荷载作用下公路桥梁振动分析研究[博士论文].上海:同济大学, 1987: 1~20
24何曙名.斜拉桥的车桥振动分析.石家庄铁道学院学报. 1991, 4(4): 109~117
25梁振辉,苏木标,王业敏.车桥耦合系统动力方程的推导.青岛建筑工程学院学报. 1992, 13(1): 18~26
26梁振辉,苏木标.车桥系统动力特性研究.青岛建筑工程学院学报. 1992, 13(4): 11~17
27程保荣,周玉勋.车桥耦合系统动力分析的模态综合技术.清华大学学报(自然科学版). 2002, 42(8): 1083~1086
28张军,江克斌,胡业平.车桥耦合动力学系统模态综合分析.解放军理工大学学报(自然科学版). 2003, 4(1): 67~70
29王潮海,王宗林.车-桥耦合振动分析的模态综合方法.公路交通科技. 2006,23(12): 76~80
30肖新标,沈火明. 3种车桥耦合振动分析模型的比较研究.西南交通大学学报. 2004, 39(2); 172~175
31杨建荣.车桥耦合作用下公路桥梁局部振动研究[博士论文].同济大学, 2007: 23~43
32万信华.斜拉桥车桥耦合振动及其MTMD振动控制[博士论文].华中科技大学, 2006: 42~47
33陈德伟,项海帆.斜张桥二阶理论的实用计算.城市道桥与防洪. 1988, 1(1): 1~12
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2 R. Cal?ada, A. Cunha, R. Delgado. Analysis of traffic-induced vibration in a cable-stayed bridge. Part I: Experimental assessment. Journal of Bridge Engineering. 2005, 10(4): 370~385
3 R. Cal?ada, A. Cunha, R. Delgado. Analysis of traffic-induced vibration in a cable-stayed bridge. Part II: Numerical modeling and stochastic simulation. Journal of Bridge Engineering. 2005, 10(4): 386~397
4 X. Shi, C. S. Cai. Vehicle induced dynamic behavior of short-span slab bridges considering effect of approach slab condition. J Bridge Engineering. 2008, 13(1): 83~92
5 H. H. Jeffcott. On the vibration of beams under the action of moving loads. Philosophical Mag. 1929, 8(48): 66~97
6 C. P. Tan. Dynamic response of a horizontally curved bridge. Journal of Struct Div. 1968a, 94(3): 761~781
7 C. P. Tan. Response of a horizontally curved bridge to moving loads. Journal of Struct Div. 1968b, 94(9): 2135~2151
8 S. Timoshenko. Vibration problems in engineering. 4th Ed. New York: Wiley, 1974: 1~10
9 G. B. Warburton. The dynamical behavior of structures. 2nd Ed. England, Oxford: Pergamon Press, 1976: 1~20
10 N. Sridharan. Numerical analysis of vibration of beams subjected to moving loads. J Sound & Vibration. 1979, 65(1): 147~150
11 T. E. Blejwas. Dynamic interaction of moving vehicles and structures. J Sound & Vibration. 1979, 67(4): 513~521
12 M. J. Inbanathan. Bridge vibrations due to vehicle moving over rough surface. J Struct Engrg. 1987, 113(9): 1994~2008
13 J. E. Akin. Numerical solution for response of beams with moving mass. J StructEngrg. 1989, 115(1): 120~131
14林海,肖盛燮.桥梁车辆振动分析理论评述.重庆交通学院学报. 1998, 17(3): 1~9
15 E. S. Hwang, A. S. Nowak. Simulation of dynamic load for bridges. J Struct Engrg. 1991, 117(5): 1413~1434
16 Ton-Lo Wang, Dongzhou Huang. Cable-stayed bridge vibration due to road surface roughness. J Struct Engrg. 1992, 118(5): 1354~1374
17 Yeong-Bin Yang, B. H. Lin. Vehicle-bridge interaction analysis by dynamic condensation method. J Struct Engrg. 1995, 121(11): 1636~1643
18 Yeong-Bin Yang, Jong-Dar Yao. Vehicle-bridge interaction element for dynamic analysis. J Struct Engrg. 1997, 123(11): 1512~1518
19 G. H. Tan, G. H. Brameld. Development of an analytical model for treating bridge-vehicle interaction. Engineering Structures. 1998, 20(1-2): 54~61
20谭国辉.车辆与桥梁相互作用的系统模拟.土木工程学报. 1996, 29(3): 34~41
21 Y. L. Xu, W. H. Guo. Dynamic analysis of coupled road vehicle and cable-stayed bridge systems under turbulent wind. Engineering Structures. 2003, 23: 473~486
22 L. Kwasniewski, Hongyi Li, Jerry Wekezer, et al. Finite element analysis of vehicle-bridge interaction. Finite Element in Analysis and Design. 2006, 42: 950~959
23毛清华.移动车辆荷载作用下公路桥梁振动分析研究[博士论文].上海:同济大学, 1987: 1~20
24何曙名.斜拉桥的车桥振动分析.石家庄铁道学院学报. 1991, 4(4): 109~117
25梁振辉,苏木标,王业敏.车桥耦合系统动力方程的推导.青岛建筑工程学院学报. 1992, 13(1): 18~26
26梁振辉,苏木标.车桥系统动力特性研究.青岛建筑工程学院学报. 1992, 13(4): 11~17
27程保荣,周玉勋.车桥耦合系统动力分析的模态综合技术.清华大学学报(自然科学版). 2002, 42(8): 1083~1086
28张军,江克斌,胡业平.车桥耦合动力学系统模态综合分析.解放军理工大学学报(自然科学版). 2003, 4(1): 67~70
29王潮海,王宗林.车-桥耦合振动分析的模态综合方法.公路交通科技. 2006,23(12): 76~80
30肖新标,沈火明. 3种车桥耦合振动分析模型的比较研究.西南交通大学学报. 2004, 39(2); 172~175
31杨建荣.车桥耦合作用下公路桥梁局部振动研究[博士论文].同济大学, 2007: 23~43
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