大跨度斜拉桥最大单悬臂施工阶段抖振响应分析
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摘要
随着经济和科技的进步,现代斜拉桥等大跨桥梁正朝着超大跨度、极度柔性方向发展,大跨度桥梁的风致振动问题显得尤为突出,已成为在设计中的主要控制因素之一。桥梁抖振是由近地风中的紊流成分引起的随机性强迫振动,抖振虽不像颤振那样引起灾难性的失稳破坏,但抖振在任何风速下都有可能发生,过大的抖振响应不仅会影响行车安全和行人的舒适度还会引起结构构件的疲劳破坏；施工阶段还会危及人员和设备的安全。因此桥梁的抖振响应逐渐引起人们的重视,成为桥梁风致振动研究的重点内容之一
本文以某大跨斜拉桥为工程背景,主要对斜拉桥施工阶段的最大单悬臂状态进行了线性抖振分析,主要工作包括以下几点：
1.根据大跨度斜拉桥的特点及脉动风场的特性,分析了大跨斜拉桥三维脉动风场简化的可行性,将三维的脉动风场简化为多个独立的一维脉动风场,并根据谐波叠加法编制了脉动风场的模拟程序。
2.将平均风引起的静风力和脉动风引起的抖振力进行时域化处理,抖振力求解采取Scanlan建议的准定常气动力模型并考虑了气动导纳的影响。对于建立的动力平衡方程,采用直接积分法中的Newmark法进行抖振响应的求解。
3.对某大跨斜拉桥最大单悬臂施工阶段进行线性抖振时域分析,并分析气动导纳的影响；最后结合本桥的风洞试验,将理论计算结果和试验结果进行了对比以检验理论计算的合理性。
4.对本论文内容进行了总结,得出了一些结论并提出需要注意的事项和不足之处,指出了研究中有待解决的问题。
The issue of wind induced vibrations of long span bridges has become one of the main dominating factors in design due to the longer span and higher flexibility. Among the various vibrations buffeting response, a forced random vibration excited by turbulence flow, is the objective of this paper. The buffeting could be excited in any wind speed, though it could not induced the instability collapse such as flutter, the comparatively large buffeting responses may cause safety and comfort of vehicles and pedestrians and may cause the structure damage due to fatigue. In erection state, the buffeting with large amplitude also needs to be controlled in order to secure the personnel and equipments from danger. Therefore, bridge buffeting responses have drawn more attention and in this way have become one of the primary research topics.
Based on a long span cable-stayed bridge, the linear buffeting analysis for single largest cantilever erection stage is conducted and the following contents are included:
1. According to the characteristics of the cable-stayed bridge and natural wind field, feasibility analysis of three-dimensional fluctuating wind field simplification is conducted by simplifying the three-dimensional gusty wind field into multiple single dimensional gusty wind fields and compiling simulation program using harmonic synthesis method.
2. The time domain transformations are conducted for buffeting loadings caused by static wind and gusty wind. The calculating of buffeting forces is achieved by quasi-steady aerodynamic model proposed by Scanlan while considering the influence of aerodynamic admittance. Established the largest single cantilever construction stage structure of the equation of motion and Newmark method which belongs to direction integral method, the solving program is established.
3. The linear buffeting analysis in time domain for a cable-stayed bridge in single largest cantilever erection stage and the influence of aerodynamic admittance to the results are conducted. Based on this, a comparison is made with results obtained in the wind tunnel tests and thus the precision of the calculating results could be verified.
4. A conclusion is made and some items that should be noticed, short comings, and the issues to be solved are discussed.
本文以某大跨斜拉桥为工程背景,主要对斜拉桥施工阶段的最大单悬臂状态进行了线性抖振分析,主要工作包括以下几点：
1.根据大跨度斜拉桥的特点及脉动风场的特性,分析了大跨斜拉桥三维脉动风场简化的可行性,将三维的脉动风场简化为多个独立的一维脉动风场,并根据谐波叠加法编制了脉动风场的模拟程序。
2.将平均风引起的静风力和脉动风引起的抖振力进行时域化处理,抖振力求解采取Scanlan建议的准定常气动力模型并考虑了气动导纳的影响。对于建立的动力平衡方程,采用直接积分法中的Newmark法进行抖振响应的求解。
3.对某大跨斜拉桥最大单悬臂施工阶段进行线性抖振时域分析,并分析气动导纳的影响；最后结合本桥的风洞试验,将理论计算结果和试验结果进行了对比以检验理论计算的合理性。
4.对本论文内容进行了总结,得出了一些结论并提出需要注意的事项和不足之处,指出了研究中有待解决的问题。
The issue of wind induced vibrations of long span bridges has become one of the main dominating factors in design due to the longer span and higher flexibility. Among the various vibrations buffeting response, a forced random vibration excited by turbulence flow, is the objective of this paper. The buffeting could be excited in any wind speed, though it could not induced the instability collapse such as flutter, the comparatively large buffeting responses may cause safety and comfort of vehicles and pedestrians and may cause the structure damage due to fatigue. In erection state, the buffeting with large amplitude also needs to be controlled in order to secure the personnel and equipments from danger. Therefore, bridge buffeting responses have drawn more attention and in this way have become one of the primary research topics.
Based on a long span cable-stayed bridge, the linear buffeting analysis for single largest cantilever erection stage is conducted and the following contents are included:
1. According to the characteristics of the cable-stayed bridge and natural wind field, feasibility analysis of three-dimensional fluctuating wind field simplification is conducted by simplifying the three-dimensional gusty wind field into multiple single dimensional gusty wind fields and compiling simulation program using harmonic synthesis method.
2. The time domain transformations are conducted for buffeting loadings caused by static wind and gusty wind. The calculating of buffeting forces is achieved by quasi-steady aerodynamic model proposed by Scanlan while considering the influence of aerodynamic admittance. Established the largest single cantilever construction stage structure of the equation of motion and Newmark method which belongs to direction integral method, the solving program is established.
3. The linear buffeting analysis in time domain for a cable-stayed bridge in single largest cantilever erection stage and the influence of aerodynamic admittance to the results are conducted. Based on this, a comparison is made with results obtained in the wind tunnel tests and thus the precision of the calculating results could be verified.
4. A conclusion is made and some items that should be noticed, short comings, and the issues to be solved are discussed.
引文
[1]项海帆.现代桥梁抗风理论与实践北京人民教育出版社2005
[2]项海帆.风工程力学和大跨桥梁的空气动力学问题.中国基金会.1994.3
[3]Scanlan.R. H. Gade R H.Motion of suspended bridge spans under gusty wind. J Struct Engrg DivASCE,1977,103(9),1867-1883
[4]R. H.Scanlan. The action of flexible bridge under wind, Ⅱ:buffeting theory J Sound and Vibration 1978,60(2,)201～211
[5]Davenport A. G Buffeting of a suspension bridge by storm winds. J. Struct Engrg Div ASCE,1962,88(6),233～264
[6]Davenport A. G The application of statistical concept to the wind loading of structures Proc,ICE,1961,19,449～472
[7]项海帆.结构风工程的现状和展望.振动工程学报,1997
[8]陈政清,项海帆.桥梁风工程北京人民教育出版社2005
[9]王伯惠.斜拉桥结构发展和中国经验北京人民交通出版社2003
[10]陈英俊,于希哲.风荷载计算北京中国铁道部1998
[11]交通部.公路桥梁抗风设计规范.北京人民教育出版社2004
[12]黄本才.结构抗风和风致计算.上海同济大学出版社2001
[13]Kaimal. J. C.eec. Spectral characteristics of surface layer turbulence, J. Royal Meterol. Soc.98,1972,593-589
[14]A. G. Davenport. The action of wind on suspension bridges.Proc., Int. Symp. On Suspension Bridges,1966
[15]R. H. Scanlan, N. P. Jones. Aeroelastic analysis of cable-stayed bridges. J. of Structure Engineering, ASCE, Vol.116(2),1990:279-297
[16]R. H. Scanlan, N. P. Jones. A form of aerodynamic admittance for use in bridge aeroelastic analysis. Journal of Fluids and Structures, Vol.13,1999:1017-1027
[17]R. H. Scanlan. On flutter and buffeting mechanisms in long-span bridges. Prob. Engrg. Mech.,1988,3(1):22-27
[18]R. H. Scanlan. Role of indicial functions in buffeting analysis of bridges. J. Structure Engineering, ASCE,Vol.110(7),1984
[19]R. H. Scanlan. Bridge deck aeroelastic admittance revisted. Journal of bridge Engineering, Vol.5(1):1-7
[20]马存明.流线箱型桥梁断面三维气动导纳研究.西南交通大学博士学位论文.2007.1
[21]孙延国.连续刚构桥最大悬臂状态风载内力及抖振实用计算方法研究.西南交通大学硕士学位论文.2008.10
[22]张晋媛.大跨斜拉桥线性抖振时域分析.西南交通大学硕士学位论文.2010.03
[23]姚伟.大跨度公铁两用斜拉桥风致抖振时域分析.西南交通大学硕士学位论文.2011.04
[24]陈伟.大跨度桥梁抖振反应谱研究.同济大学博士学位论文.1993
[25]项海帆,陈伟等.桥梁抖振反应谱的实用方法.同济大学土木工程学报.1995.
[26]Matsumoto M, Chen X, Shiraishi N.Buffeting analysis of long spanbridge with aerodynamic coupling. Proceedings of 13 th National Symp on Wind Engrg, Japan Association for Wind Engineering,1994,227～232(in Japanese)
[27]Chen X, Matsumoto M, Kareem A. Aerodynamic coupled effects on flutter and buffeting of bridge. J. Engrg.Mech. ASCE,200,126(1),17～26
[28]Jain A, Jones N P, Scanlan R. H. Coupled flutter and buffeting analysis of long-span bridge. J. Struct. Engrg,ASCE,1996,122(7),716～725
[29]Jones N P, Jain A, Scanlan R. H. Wind cross-spectrum effects on long-span bridges. Proceedings of Engrg Mech Spec Conf ASCE, New York.1992
[30]Minh N N, Miyata T,Yamada H, Sanada Y Numerical simulation of wind turbulence and buffeting analysis of long-span bridge. J. Wind Engineering & Industrial Aerodynamics.1999,83,301,315
[31]李明水.连续大气湍流中大跨度桥梁的抖振响应.西南交通大学博士学位论文.1993
[32]李明水,贺德馨,王卫华.大跨度桥梁抖振响应的频域分析.空气动力学学报.2000.03.
[33]丁泉顺.大跨度桥梁耦合颤抖振响应分析.同济大学博士学位论文.2007
[34]王志强.铁路斜拉桥施工阶段抖振响应分析.西南交通大学硕士学位论文.2011
[35]Lin Y K, Motion of suspension-bridge in turbulent winds. Journal of Engineering Mech. Div.ASDE,1979.105(6):921-932
[36]Lin Y K, Ariaratnaam S T. Stability of bridge motion in turbulen flow. Journal of Structure Mech. ASDE,1980,8(1):1-15
[37]周述华.大跨度悬索桥空间非线性抖振响应时程分析.西南交通大学博士学位论文.1993
[38]刘春华.大跨度桥梁抖振响应的非线性时程分析.同济大学博士学位论文.1995
[39]曹映泓.大跨度桥梁非线性颤振和抖振时程分析.同济大学博士学位论文.1999
[40]王之宏.风荷载的模拟研究.建筑结构学报.1994,15(1)：44-52
[41]李永乐,周述华,强士中.大跨度斜拉桥三维脉动风场模拟，土木工程学报,2003,36(10)：60-65
[42]曹映泓,项海帆等.大跨度桥梁随机风场的模拟.土木工程学报.Vo1.31(3),1998(6)
[43]孙刘军.大跨度钢桁梁拱桥时域分析.西南交通大学硕士学位论文.2009.
[44]G. Deodatis. Simulation of ergodic multivariate stochastic processes. J. Engineering Mechanics, ASCE,122(8),1996,778-787
[45]M. Shinozuka, C. B.Yun, H. Seya. Stochastic methods in wind engineering. J. Wind Engineering and Industrial Aerodynamics.1990(36).829-843
[46]N. N. Minh, T. Miyata. H. Yamada. Y. Sanada. Numerical simulation of wind turbulence and buffeting analysis of long-span bridge. J. Wind Engineering and Industrial Aerodynamics,1999,83:301-315.
[47]M. D. Paola. Digital simulation of wind field velocity. J. Wind Engineering and Industrial Aerodynamics,1998(74-76),91-109
[48]Y. Li, A. Kareem. Simulation of multivariate random processes:hybrid DFT and digital filtering approach. J Engineering Mechanics, Vol.119(3),1993,1078-1098
[49]Shinozuka M, Deodatis G. Simulation of stochastic processes by spectral respresentation.[J]. Appl Mech Rev.1991,44(4):191-203
[50]Sears W.R.Some aspects of non-stationary airfoil theory and its practical application.J.Aeronauticaol science,1941,8(3)
[51]曾宪武,韩大建.大跨桥梁风致抖振时域分析在ANSYS中的实现.桥梁建设,2004(1)：9-12
[52]胡晓论.大跨度斜拉桥颤抖振响应及静风稳定性分析.同济大学博士学位论文.2006
[53]刘兰殉.浅谈集中质量矩阵和一致质量矩阵.中国科技论文在线.2006
[54]杨亚平,沈海宁.集中质量矩阵代替一致质量矩阵的合理性和局限性.青海大学学报.2008.02
[2]项海帆.风工程力学和大跨桥梁的空气动力学问题.中国基金会.1994.3
[3]Scanlan.R. H. Gade R H.Motion of suspended bridge spans under gusty wind. J Struct Engrg DivASCE,1977,103(9),1867-1883
[4]R. H.Scanlan. The action of flexible bridge under wind, Ⅱ:buffeting theory J Sound and Vibration 1978,60(2,)201～211
[5]Davenport A. G Buffeting of a suspension bridge by storm winds. J. Struct Engrg Div ASCE,1962,88(6),233～264
[6]Davenport A. G The application of statistical concept to the wind loading of structures Proc,ICE,1961,19,449～472
[7]项海帆.结构风工程的现状和展望.振动工程学报,1997
[8]陈政清,项海帆.桥梁风工程北京人民教育出版社2005
[9]王伯惠.斜拉桥结构发展和中国经验北京人民交通出版社2003
[10]陈英俊,于希哲.风荷载计算北京中国铁道部1998
[11]交通部.公路桥梁抗风设计规范.北京人民教育出版社2004
[12]黄本才.结构抗风和风致计算.上海同济大学出版社2001
[13]Kaimal. J. C.eec. Spectral characteristics of surface layer turbulence, J. Royal Meterol. Soc.98,1972,593-589
[14]A. G. Davenport. The action of wind on suspension bridges.Proc., Int. Symp. On Suspension Bridges,1966
[15]R. H. Scanlan, N. P. Jones. Aeroelastic analysis of cable-stayed bridges. J. of Structure Engineering, ASCE, Vol.116(2),1990:279-297
[16]R. H. Scanlan, N. P. Jones. A form of aerodynamic admittance for use in bridge aeroelastic analysis. Journal of Fluids and Structures, Vol.13,1999:1017-1027
[17]R. H. Scanlan. On flutter and buffeting mechanisms in long-span bridges. Prob. Engrg. Mech.,1988,3(1):22-27
[18]R. H. Scanlan. Role of indicial functions in buffeting analysis of bridges. J. Structure Engineering, ASCE,Vol.110(7),1984
[19]R. H. Scanlan. Bridge deck aeroelastic admittance revisted. Journal of bridge Engineering, Vol.5(1):1-7
[20]马存明.流线箱型桥梁断面三维气动导纳研究.西南交通大学博士学位论文.2007.1
[21]孙延国.连续刚构桥最大悬臂状态风载内力及抖振实用计算方法研究.西南交通大学硕士学位论文.2008.10
[22]张晋媛.大跨斜拉桥线性抖振时域分析.西南交通大学硕士学位论文.2010.03
[23]姚伟.大跨度公铁两用斜拉桥风致抖振时域分析.西南交通大学硕士学位论文.2011.04
[24]陈伟.大跨度桥梁抖振反应谱研究.同济大学博士学位论文.1993
[25]项海帆,陈伟等.桥梁抖振反应谱的实用方法.同济大学土木工程学报.1995.
[26]Matsumoto M, Chen X, Shiraishi N.Buffeting analysis of long spanbridge with aerodynamic coupling. Proceedings of 13 th National Symp on Wind Engrg, Japan Association for Wind Engineering,1994,227～232(in Japanese)
[27]Chen X, Matsumoto M, Kareem A. Aerodynamic coupled effects on flutter and buffeting of bridge. J. Engrg.Mech. ASCE,200,126(1),17～26
[28]Jain A, Jones N P, Scanlan R. H. Coupled flutter and buffeting analysis of long-span bridge. J. Struct. Engrg,ASCE,1996,122(7),716～725
[29]Jones N P, Jain A, Scanlan R. H. Wind cross-spectrum effects on long-span bridges. Proceedings of Engrg Mech Spec Conf ASCE, New York.1992
[30]Minh N N, Miyata T,Yamada H, Sanada Y Numerical simulation of wind turbulence and buffeting analysis of long-span bridge. J. Wind Engineering & Industrial Aerodynamics.1999,83,301,315
[31]李明水.连续大气湍流中大跨度桥梁的抖振响应.西南交通大学博士学位论文.1993
[32]李明水,贺德馨,王卫华.大跨度桥梁抖振响应的频域分析.空气动力学学报.2000.03.
[33]丁泉顺.大跨度桥梁耦合颤抖振响应分析.同济大学博士学位论文.2007
[34]王志强.铁路斜拉桥施工阶段抖振响应分析.西南交通大学硕士学位论文.2011
[35]Lin Y K, Motion of suspension-bridge in turbulent winds. Journal of Engineering Mech. Div.ASDE,1979.105(6):921-932
[36]Lin Y K, Ariaratnaam S T. Stability of bridge motion in turbulen flow. Journal of Structure Mech. ASDE,1980,8(1):1-15
[37]周述华.大跨度悬索桥空间非线性抖振响应时程分析.西南交通大学博士学位论文.1993
[38]刘春华.大跨度桥梁抖振响应的非线性时程分析.同济大学博士学位论文.1995
[39]曹映泓.大跨度桥梁非线性颤振和抖振时程分析.同济大学博士学位论文.1999
[40]王之宏.风荷载的模拟研究.建筑结构学报.1994,15(1)：44-52
[41]李永乐,周述华,强士中.大跨度斜拉桥三维脉动风场模拟，土木工程学报,2003,36(10)：60-65
[42]曹映泓,项海帆等.大跨度桥梁随机风场的模拟.土木工程学报.Vo1.31(3),1998(6)
[43]孙刘军.大跨度钢桁梁拱桥时域分析.西南交通大学硕士学位论文.2009.
[44]G. Deodatis. Simulation of ergodic multivariate stochastic processes. J. Engineering Mechanics, ASCE,122(8),1996,778-787
[45]M. Shinozuka, C. B.Yun, H. Seya. Stochastic methods in wind engineering. J. Wind Engineering and Industrial Aerodynamics.1990(36).829-843
[46]N. N. Minh, T. Miyata. H. Yamada. Y. Sanada. Numerical simulation of wind turbulence and buffeting analysis of long-span bridge. J. Wind Engineering and Industrial Aerodynamics,1999,83:301-315.
[47]M. D. Paola. Digital simulation of wind field velocity. J. Wind Engineering and Industrial Aerodynamics,1998(74-76),91-109
[48]Y. Li, A. Kareem. Simulation of multivariate random processes:hybrid DFT and digital filtering approach. J Engineering Mechanics, Vol.119(3),1993,1078-1098
[49]Shinozuka M, Deodatis G. Simulation of stochastic processes by spectral respresentation.[J]. Appl Mech Rev.1991,44(4):191-203
[50]Sears W.R.Some aspects of non-stationary airfoil theory and its practical application.J.Aeronauticaol science,1941,8(3)
[51]曾宪武,韩大建.大跨桥梁风致抖振时域分析在ANSYS中的实现.桥梁建设,2004(1)：9-12
[52]胡晓论.大跨度斜拉桥颤抖振响应及静风稳定性分析.同济大学博士学位论文.2006
[53]刘兰殉.浅谈集中质量矩阵和一致质量矩阵.中国科技论文在线.2006
[54]杨亚平,沈海宁.集中质量矩阵代替一致质量矩阵的合理性和局限性.青海大学学报.2008.02