基于曲率模态理论的先简支后连续梁桥损伤识别研究
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摘要
桥梁在其建造及服务期间不可避免地要受到环境及有害物质的侵蚀,诸如超重车、地震、结构疲劳、材料老化、构件缺陷以及人为破坏等,会造成桥梁不同程度的损伤,降低桥梁的实际承载力。桥梁因存在结构缺陷和损伤而垮塌的事件时有发生,对桥梁进行有效的长期健康监测、定期安全评价和针对性的维护加固,保障桥梁安全使用已成为桥梁管理运营部门最为关注的问题。本文以交通部颁布的20m至40mT梁和箱梁的通用图为基础,首先建立先简支后连续梁桥有限元模型,数值计算连续梁的模态参数,且系统计算分析不同截面、不同跨径和不同跨数对连续梁自振特性的影响。其次对基于曲率模态理论桥梁结构损伤识别方法进行研究,研究结果表明：
1、曲率模态法、曲率模态微分法、曲率模态绝对差法均能对结构损伤进行识别,且低阶模态出现误导小峰的概率较小,损伤识别效果较好,其中曲率模态绝对差识别效果又优于另两类方法,而曲率模态微分法则不需要桥梁原始数据即可对结构进行损伤识别。
2、以曲率模态理论为基础的三类识别方法的识别效果与桥梁振型选取有关,当损伤位置位于振型节点附近时,则无法识别。
3、在单处损伤识别中,曲率模态绝对差曲线在损伤位置处会有突变,突变程度与损伤程度有关,损伤程度越大,突变越明显。对于存在多处损伤的结构,相同损伤程度且不同位置的曲率模态绝对差增量不同,相互独立,曲率模态绝对差能够判定损伤程度大小。
4、基于频率的损伤识别方法依赖桥梁的原始数据。频率的变化中可以评定结构是否存在损伤,但无法判断损伤位置和损伤程度。
The bridges are corroded by the environment and harmful substances during the construction and service inevitably, such as overload, earthquake, the structure fatigue, material aging, defect and man-made sabotage, causing the damage of different degree and reducing the actual bearing capacity of the bridges. The bridges often collapse due to the presence of structural defects and damages. The effective long-term health monitoring, regular safety evaluation and the reinforcement for the bridges to ensure the safety of the bridges have become the most concerned problems for the departments of bridge management. In this paper, the simply-supported continuous bridge model was set up based on20m to40m general diagram produced by the ministry of communications, the modal parameters of the continuous beam was obtained by numerical calculation and studying the impact of different section, different span and different span number on natural vibration characteristics of the bridge. And the damage identification of the bridges was studied based on curvature mode theory, the results show:
1、Modal curvature method, the curvature modal differential method and absolute deviation of curvature modal method are all able to identify the damage of the bridge, the probability of small misleading peal appears in the low order modes is small. The effect of damage identification is good. The curvature modal absolute difference recognition effect is better than the other two kinds of methods. Curvature modal differential method does not need the raw data of the bridge to identify the damage of the structure.
2、The three kinds of identification methods based on curvature mode theory are all relating to the selection of bridge vibration mode. When the location of damages is near the nodes of mode shape, the three kinds of methods could not identify the damages.
3、In the single damage identification, absolute deviation of curvature curve will have a mutation at the damage location. Degree of mutations associated with damage degree, damage degree, the more obvious mutation. The structure with several damages, under the same damage degree condition, absolute deviation of curvature modal of the increment of different positions is different and independent. Absolute deviation of curvature modal method could identify the damage degree.
4、The damage identification method based on the changes of frequencies depends on the raw data of the bridge. We could identify the damages of the structure by the changes of frequencies, but we can not decide the damage location and degree of the damage.
1、曲率模态法、曲率模态微分法、曲率模态绝对差法均能对结构损伤进行识别,且低阶模态出现误导小峰的概率较小,损伤识别效果较好,其中曲率模态绝对差识别效果又优于另两类方法,而曲率模态微分法则不需要桥梁原始数据即可对结构进行损伤识别。
2、以曲率模态理论为基础的三类识别方法的识别效果与桥梁振型选取有关,当损伤位置位于振型节点附近时,则无法识别。
3、在单处损伤识别中,曲率模态绝对差曲线在损伤位置处会有突变,突变程度与损伤程度有关,损伤程度越大,突变越明显。对于存在多处损伤的结构,相同损伤程度且不同位置的曲率模态绝对差增量不同,相互独立,曲率模态绝对差能够判定损伤程度大小。
4、基于频率的损伤识别方法依赖桥梁的原始数据。频率的变化中可以评定结构是否存在损伤,但无法判断损伤位置和损伤程度。
The bridges are corroded by the environment and harmful substances during the construction and service inevitably, such as overload, earthquake, the structure fatigue, material aging, defect and man-made sabotage, causing the damage of different degree and reducing the actual bearing capacity of the bridges. The bridges often collapse due to the presence of structural defects and damages. The effective long-term health monitoring, regular safety evaluation and the reinforcement for the bridges to ensure the safety of the bridges have become the most concerned problems for the departments of bridge management. In this paper, the simply-supported continuous bridge model was set up based on20m to40m general diagram produced by the ministry of communications, the modal parameters of the continuous beam was obtained by numerical calculation and studying the impact of different section, different span and different span number on natural vibration characteristics of the bridge. And the damage identification of the bridges was studied based on curvature mode theory, the results show:
1、Modal curvature method, the curvature modal differential method and absolute deviation of curvature modal method are all able to identify the damage of the bridge, the probability of small misleading peal appears in the low order modes is small. The effect of damage identification is good. The curvature modal absolute difference recognition effect is better than the other two kinds of methods. Curvature modal differential method does not need the raw data of the bridge to identify the damage of the structure.
2、The three kinds of identification methods based on curvature mode theory are all relating to the selection of bridge vibration mode. When the location of damages is near the nodes of mode shape, the three kinds of methods could not identify the damages.
3、In the single damage identification, absolute deviation of curvature curve will have a mutation at the damage location. Degree of mutations associated with damage degree, damage degree, the more obvious mutation. The structure with several damages, under the same damage degree condition, absolute deviation of curvature modal of the increment of different positions is different and independent. Absolute deviation of curvature modal method could identify the damage degree.
4、The damage identification method based on the changes of frequencies depends on the raw data of the bridge. We could identify the damages of the structure by the changes of frequencies, but we can not decide the damage location and degree of the damage.
引文
[1]张德文,魏埠旋.模型修正与破损诊断.北京：科学出版社,1999
[2]Bapat A V, Venkatraman N. New Approach for The Representation of A Point Support in The Analysis of Plates. Journal of Sound and Vibration. 1998,120(1):107-125
[3]刘蕾蕾.基于曲率模态分析的梁桥损伤识别研究.西南交通大学硕士论文,2007,5
[4]Andersen E Y, Pedersen. Structural monitoring of the Great Belt East Bridge. In:Jon Krokeborg, ed. Proceedings of the Third Symposium on Strait Crossing. Rotterdam:Balkema,1999,54-62
[5]袁万城,崔飞.张启伟.桥梁健康监测与状态评估的研究现状与发展.同济大学学报,1999,27：184—188
[6]Muria Vila D, Gomez R, King C. Dynamic Structural properties of cable stayed Tampico Bridge. Journal of Structural Engineering, ASCE,1991,117(11):3396-3416
[7]Myroll F, Dibiagio E. Instrumentation for monitoring the Skarnunder Cable-stayed Bridge. In:Jon Krokeborg, ed. Proceedings of the Third Symposium on Strait Crossing. Rotterdam:Balkema,1994.207-215
[8]Curran P, Tilly G. Design and monitoring of the Flintshire Bridge, UK[J].Structural Engineering International,1999,3:225-228
[9]chueng M S, Tadros G S, Brown T G, er al. Field monitoring and research on performance of the Confederation Bridge[J]. Canadian Journal of Civil Engineering,1997,24(6):951-962
[10]Lau C K, Mak W P N, Wong K Y, et al. Structural health monitoring of three cable-supported bridges in Hong Kong[A]. Chang F K. Structural Health Monitoring 2000[C].Pennsylvania:Technomic Publishing Co,1999:450-460
[11]史家钧,项海帆,许俊.确保大型桥梁安全性与耐久性的综合监测系统。同济大学学报,1997,25(增刊)：71-75
[12]刘继承,周传荣.一个基于优化的有限元模型修正方法[J].冲击与振动,2003,22(2)：33—34
[13]夏品奇,James M W Brownjohn.斜拉桥有限元建模与模型修正[J].振动工 程学报,2003,16(2)：219—223
[14]蒋华.基于静力测试数据的桥梁结构损伤识别与评定理论研究[D].四川成都：西南交通大学博士学位论文,2005
[15]杜思义.基于频率变化与单元摄动理论的结构损伤识别方法研究[D].重庆：重庆大学博士学位论文,2005
[16]向天宇,赵人达,刘海波.基于静力测试数据的预应力混凝土连续梁结构损伤识别[J].土木工程学报,2003,36(11)：79-82
[17]蔡晶,吴智深,李兆霞.静力荷载作用下结构参数识别及状态评估的统计分析[J].工程力学,2004,21(6)：76-83
[18]张清华,李乔,唐亮.斜拉桥结构损伤识别的概率可靠度法[J].铁道学报.2005,27(3)：70-75
[19]崔飞,袁万城.基于静态应变及位移测量的结构损伤识别法[J].同济大学学报,2000,28(1)：5-8
[20]Sanayei m, Saletnik M. J. Parametre estimation of structures from static strain measurements I:Formulation[J]. Journal of structural engineering,1996,122(5):555-562
[21]Banan M R, Hjelmstad K D. Parametre estimation of structures from static response I:computational aspects [J]. Journal of structural Engineering,1994,120(11):3243-3258
[22]Hajela P, Soero F J. Recent developments in damage detection based on system indentification metheods[J]. Structural Optimization,1990(2):1-10
[23]张启伟,范立础.利用动静力测量数据的桥梁结构损伤识别[J].同济大学学报,1998,26：528-532
[24]Ratcliffe C P, Damage detection using a modified Laplacian operator on mode shape data[J]. Journal of Sound and Vibration, 1998,204(3):505-517
[25]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shape[J]. Journal of Sound and Vibration, 1991,145(2):321-332
[26]李德葆,陆秋海,秦权.承弯结构的曲率模态分析[J].清华大学学报(自然科学版),2002,42(2)：224-227
[27]邓焱.梁及桥梁应变模态与损伤测量的新方法[J].清华大学学报(自然科学版),2000,40(11)：123-127
[28]郑明刚,刘天雄,朱继梅等.曲率模态在桥梁状态监测中的应用[J].振动与冲击,2000,19(2)：81-83
[29]Jenks W G. Squids for nondestructive evaluation [J]. Journal of Physics & Applied Physics,1997,30(3):293-323
[30]Salawn 0 S.Damage location using vibration mode shapes[C]. Proceedings of 12th IMAC,1994:933-939
[31]Pandey AK, Biswas M. Damage detection from changes in flexibility[J]. Journal of Sound and Vibration,1994,169(1):3-17
[32]伊娟.基于柔度改变的连续梁桥损伤诊断研究[J].华东公路,2001(3)：25-27
[33]慕宝晖,邬瑞锋,蔡贤辉,李桂华.一种桁架结构损伤识别的柔度阵法[J].计算力学学报,2001,18(1)：42-47
[34]Huang T J. Structural damaged detection using energy transfer ratio[C]. Proceedings of 14th IMAC,1996:26-132
[35]Liang Z. On detection of damage location of bridges[C]. Proceedings of IMAC,1996:308-312
[36]Ceasar J C. Damage location in a space truss model using modal strain energy[C]. Proceedings of 15th IMAC, Florida,1997:1786-1792
[37]史治宇.结构破损定位的单元模态应变能变化率法[J].振动工程学报,1998,11(3)：357-360
[38]李国强,李杰.《工程结构动力检测理论与应用》北京.科学出版社,2002
[39]F Saleh,B Supriyadi,B Suhendro, D Tran. Damage Detection In Non-prismatic Reinforced Concrete Beams Using Curvature Mode Shapes[J].Structural Integrity and Fracture,2004,119-124
[40]Doebling SW, Farrar CR, Prime MB. A summary review of vibration-based damage identification methods. The shock and Vibration Digest,1998,30(2):91-105
[41]顾培英.基于应变模态技术的结构损伤诊断直接指标法研究[D].河海大学,博士学位论文,2006.
[42]陈江,熊峰.基于曲率模态振型的损伤识别方法研究[J].武汉理工大学党报.2007,29(3)：99—102
[43]曹树谦,张文德.振动结构模态分析。天津：天津大学出版社,2001.
[44]应怀樵.现代振动与噪声技术(第4卷)。航空工业出版社,2005.10.
[45]李德葆,陆秋海.实验模态分析及应用。北京：科学出版社,2001
[46]刘景生.设计荷载作用下先简支后连续小箱梁桥的内力分析。西南交通大学硕士学位论文。2008
[47]陈强.先简支后连续结构体系研究。浙江大学博士学位论文。2002
[48]陈强,黄志义.先简支后连续结构体系的概念及发展。铁道建筑。2005
[49]刘国慧.简支变连续桥梁的设计与实验研究。天津大学硕士学位论文。2006
[50]胡肇滋.桥跨结构简化分析荷载横向分布[J]北京：人民交通出版社,1996,7：44—49.
[2]Bapat A V, Venkatraman N. New Approach for The Representation of A Point Support in The Analysis of Plates. Journal of Sound and Vibration. 1998,120(1):107-125
[3]刘蕾蕾.基于曲率模态分析的梁桥损伤识别研究.西南交通大学硕士论文,2007,5
[4]Andersen E Y, Pedersen. Structural monitoring of the Great Belt East Bridge. In:Jon Krokeborg, ed. Proceedings of the Third Symposium on Strait Crossing. Rotterdam:Balkema,1999,54-62
[5]袁万城,崔飞.张启伟.桥梁健康监测与状态评估的研究现状与发展.同济大学学报,1999,27：184—188
[6]Muria Vila D, Gomez R, King C. Dynamic Structural properties of cable stayed Tampico Bridge. Journal of Structural Engineering, ASCE,1991,117(11):3396-3416
[7]Myroll F, Dibiagio E. Instrumentation for monitoring the Skarnunder Cable-stayed Bridge. In:Jon Krokeborg, ed. Proceedings of the Third Symposium on Strait Crossing. Rotterdam:Balkema,1994.207-215
[8]Curran P, Tilly G. Design and monitoring of the Flintshire Bridge, UK[J].Structural Engineering International,1999,3:225-228
[9]chueng M S, Tadros G S, Brown T G, er al. Field monitoring and research on performance of the Confederation Bridge[J]. Canadian Journal of Civil Engineering,1997,24(6):951-962
[10]Lau C K, Mak W P N, Wong K Y, et al. Structural health monitoring of three cable-supported bridges in Hong Kong[A]. Chang F K. Structural Health Monitoring 2000[C].Pennsylvania:Technomic Publishing Co,1999:450-460
[11]史家钧,项海帆,许俊.确保大型桥梁安全性与耐久性的综合监测系统。同济大学学报,1997,25(增刊)：71-75
[12]刘继承,周传荣.一个基于优化的有限元模型修正方法[J].冲击与振动,2003,22(2)：33—34
[13]夏品奇,James M W Brownjohn.斜拉桥有限元建模与模型修正[J].振动工 程学报,2003,16(2)：219—223
[14]蒋华.基于静力测试数据的桥梁结构损伤识别与评定理论研究[D].四川成都：西南交通大学博士学位论文,2005
[15]杜思义.基于频率变化与单元摄动理论的结构损伤识别方法研究[D].重庆：重庆大学博士学位论文,2005
[16]向天宇,赵人达,刘海波.基于静力测试数据的预应力混凝土连续梁结构损伤识别[J].土木工程学报,2003,36(11)：79-82
[17]蔡晶,吴智深,李兆霞.静力荷载作用下结构参数识别及状态评估的统计分析[J].工程力学,2004,21(6)：76-83
[18]张清华,李乔,唐亮.斜拉桥结构损伤识别的概率可靠度法[J].铁道学报.2005,27(3)：70-75
[19]崔飞,袁万城.基于静态应变及位移测量的结构损伤识别法[J].同济大学学报,2000,28(1)：5-8
[20]Sanayei m, Saletnik M. J. Parametre estimation of structures from static strain measurements I:Formulation[J]. Journal of structural engineering,1996,122(5):555-562
[21]Banan M R, Hjelmstad K D. Parametre estimation of structures from static response I:computational aspects [J]. Journal of structural Engineering,1994,120(11):3243-3258
[22]Hajela P, Soero F J. Recent developments in damage detection based on system indentification metheods[J]. Structural Optimization,1990(2):1-10
[23]张启伟,范立础.利用动静力测量数据的桥梁结构损伤识别[J].同济大学学报,1998,26：528-532
[24]Ratcliffe C P, Damage detection using a modified Laplacian operator on mode shape data[J]. Journal of Sound and Vibration, 1998,204(3):505-517
[25]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shape[J]. Journal of Sound and Vibration, 1991,145(2):321-332
[26]李德葆,陆秋海,秦权.承弯结构的曲率模态分析[J].清华大学学报(自然科学版),2002,42(2)：224-227
[27]邓焱.梁及桥梁应变模态与损伤测量的新方法[J].清华大学学报(自然科学版),2000,40(11)：123-127
[28]郑明刚,刘天雄,朱继梅等.曲率模态在桥梁状态监测中的应用[J].振动与冲击,2000,19(2)：81-83
[29]Jenks W G. Squids for nondestructive evaluation [J]. Journal of Physics & Applied Physics,1997,30(3):293-323
[30]Salawn 0 S.Damage location using vibration mode shapes[C]. Proceedings of 12th IMAC,1994:933-939
[31]Pandey AK, Biswas M. Damage detection from changes in flexibility[J]. Journal of Sound and Vibration,1994,169(1):3-17
[32]伊娟.基于柔度改变的连续梁桥损伤诊断研究[J].华东公路,2001(3)：25-27
[33]慕宝晖,邬瑞锋,蔡贤辉,李桂华.一种桁架结构损伤识别的柔度阵法[J].计算力学学报,2001,18(1)：42-47
[34]Huang T J. Structural damaged detection using energy transfer ratio[C]. Proceedings of 14th IMAC,1996:26-132
[35]Liang Z. On detection of damage location of bridges[C]. Proceedings of IMAC,1996:308-312
[36]Ceasar J C. Damage location in a space truss model using modal strain energy[C]. Proceedings of 15th IMAC, Florida,1997:1786-1792
[37]史治宇.结构破损定位的单元模态应变能变化率法[J].振动工程学报,1998,11(3)：357-360
[38]李国强,李杰.《工程结构动力检测理论与应用》北京.科学出版社,2002
[39]F Saleh,B Supriyadi,B Suhendro, D Tran. Damage Detection In Non-prismatic Reinforced Concrete Beams Using Curvature Mode Shapes[J].Structural Integrity and Fracture,2004,119-124
[40]Doebling SW, Farrar CR, Prime MB. A summary review of vibration-based damage identification methods. The shock and Vibration Digest,1998,30(2):91-105
[41]顾培英.基于应变模态技术的结构损伤诊断直接指标法研究[D].河海大学,博士学位论文,2006.
[42]陈江,熊峰.基于曲率模态振型的损伤识别方法研究[J].武汉理工大学党报.2007,29(3)：99—102
[43]曹树谦,张文德.振动结构模态分析。天津：天津大学出版社,2001.
[44]应怀樵.现代振动与噪声技术(第4卷)。航空工业出版社,2005.10.
[45]李德葆,陆秋海.实验模态分析及应用。北京：科学出版社,2001
[46]刘景生.设计荷载作用下先简支后连续小箱梁桥的内力分析。西南交通大学硕士学位论文。2008
[47]陈强.先简支后连续结构体系研究。浙江大学博士学位论文。2002
[48]陈强,黄志义.先简支后连续结构体系的概念及发展。铁道建筑。2005
[49]刘国慧.简支变连续桥梁的设计与实验研究。天津大学硕士学位论文。2006
[50]胡肇滋.桥跨结构简化分析荷载横向分布[J]北京：人民交通出版社,1996,7：44—49.