斜拉拱桥模型试验模态分析及拉索对模态参数影响研究
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摘要
斜拉拱桥是以斜拉桥和拱桥为基础的新型组合桥,它的整体结构力学性能特别是动力性能非常复杂。而动力性能是进行桥梁结构振动响应、抗震和抗风稳定性分析的基础,是桥梁结构动力学问题的重要内容。对于如此复杂的新型结构,仅仅根据理论研究是不够的,必须在理论研究的同时,通过试验研究来验证理论的正确性。不仅如此,识别出系统的模态参数,还可以为结构的损伤识别和预报以及结构动力特性的优化设计提供依据。本论文在此背景下对斜拉拱桥模型进行了试验模态分析,主要做了以下工作:
(1)利用相似理论分析了湘潭湘江四桥模型的动力相似准则,利用模态分析理论得出各模态参数的相似比,进一步探讨了实际模型在近似满足动力相似下的相似关系,得到了理想与实际两种条件下各模态参数的相似比值。然后用有限元软件ANSYS按照相似比的不同分别建立三种模型:实桥,理想模型,实际模型。算得它们的模态参数和相似比值,验证前述模态参数相似关系的正确性。
(2)按照试验模态分析的步骤,选择合适的激振方式和传感器并对系统进行校准后,用模态分离技术激振、变时基方式采样,得到各个测点的时程信号。对FFT变换得到的频域信号进行传递函数估计,然后用频域法拟合出系统的模态参数。
(3)对传递函数进行逆傅立叶变换(IFFT),得到脉冲响应函数,用时域方法特征系统实现算法(ERA)编制程序XLGQ-ERA计算出模态参数,并与频域法得到的模态频率做比较验证。用模态判定准则(MAC)对振型进行模型验证。
(4)按8种工况分别做试验模态分析:改变拉索索力,研究索力变化对结构模态参数的影响;依次减少拉索根数,直到全部拉索去掉,研究拉索有无和拉索密疏对模态参数影响。并根据拉索对模态参数的影响,提出了建议。
Cable-stayed arch bridge is a new type of composite bridge which has taken advantage of both cable-stayed bridge and arch bridge. Its integral structure mechanical performance and especially dynamic performance appear more complicated. However, dynamic behavior, which is the foundation to carry out the analysis of structure vibration response, seismic resistant, stability of wind resistant, is the important aspect of bridge dynamic mechanical problem. In order to validate the theory in such a complicated structure, only the theory research is insufficient and the experiment research is also extremely necessary. And further more, the modal parameters identified in the system are available to recognize and predict the damage in the structure and provide the basis for the optimum design of structure dynamic characteristics. Under the above background, this paper conducts the experiment mode analysis of cable-stayed arch bridge, and main accomplishments are listed as follows:
(1)The dynamic similarity criterion of Xiangtan Xiangjiang river has been analyzed by similarity theory; Similarity ratio of each modal parameters has been obtained by modal analysis theory; In addition, similarity relationship of real model which approximately satisfies dynamic similarity has been further investigated, and the similarity ratios of each ideal parameter to actual modal parameter have been gained. Finally, three kinds of models: real bridge, ideal model and theory model are established in finite element analysis software ANSYS. Their modal parameters and similarity ratios have been calculated and obtained, which validates above-mentioned relationships of mode parameters and similarity ratios.
(2)According to the procedure of experiment modal analysis, choosing appropriate excitation mode and the sensor and adjusting the system, the paper obtains time signals of every test points using the sampling technique of modal separation excitation and time base variation. And then the paper employs estimation of transfer function in the frequency-domain signals which are converted from FFT. Finally, the paper fits modal parameters of system through the frequency-domain method.
(3)Impulse response function is obtained through the IFFT transformation of the transfer function. And then the modal parameter is calculated through characteristic Economy Realization Arithmetic of time base method (ERA), which is compared with the modal frequency obtained from the method of frequency domain. The MAC is used to validate vibration mode of model.
(4)Experimental modal analysis of 8 working conditions is conducted: the tension of the cables is changed in order to study the effect of the variation of the cable's tension on the structure mode parameter; The number of the cables is gradually reduced to zero, so as to study the effect of the existence and density of cable on the mode parameters. In addition, according to the effect of the cable on the mode parameters, some suggestions are proposed.
(1)利用相似理论分析了湘潭湘江四桥模型的动力相似准则,利用模态分析理论得出各模态参数的相似比,进一步探讨了实际模型在近似满足动力相似下的相似关系,得到了理想与实际两种条件下各模态参数的相似比值。然后用有限元软件ANSYS按照相似比的不同分别建立三种模型:实桥,理想模型,实际模型。算得它们的模态参数和相似比值,验证前述模态参数相似关系的正确性。
(2)按照试验模态分析的步骤,选择合适的激振方式和传感器并对系统进行校准后,用模态分离技术激振、变时基方式采样,得到各个测点的时程信号。对FFT变换得到的频域信号进行传递函数估计,然后用频域法拟合出系统的模态参数。
(3)对传递函数进行逆傅立叶变换(IFFT),得到脉冲响应函数,用时域方法特征系统实现算法(ERA)编制程序XLGQ-ERA计算出模态参数,并与频域法得到的模态频率做比较验证。用模态判定准则(MAC)对振型进行模型验证。
(4)按8种工况分别做试验模态分析:改变拉索索力,研究索力变化对结构模态参数的影响;依次减少拉索根数,直到全部拉索去掉,研究拉索有无和拉索密疏对模态参数影响。并根据拉索对模态参数的影响,提出了建议。
Cable-stayed arch bridge is a new type of composite bridge which has taken advantage of both cable-stayed bridge and arch bridge. Its integral structure mechanical performance and especially dynamic performance appear more complicated. However, dynamic behavior, which is the foundation to carry out the analysis of structure vibration response, seismic resistant, stability of wind resistant, is the important aspect of bridge dynamic mechanical problem. In order to validate the theory in such a complicated structure, only the theory research is insufficient and the experiment research is also extremely necessary. And further more, the modal parameters identified in the system are available to recognize and predict the damage in the structure and provide the basis for the optimum design of structure dynamic characteristics. Under the above background, this paper conducts the experiment mode analysis of cable-stayed arch bridge, and main accomplishments are listed as follows:
(1)The dynamic similarity criterion of Xiangtan Xiangjiang river has been analyzed by similarity theory; Similarity ratio of each modal parameters has been obtained by modal analysis theory; In addition, similarity relationship of real model which approximately satisfies dynamic similarity has been further investigated, and the similarity ratios of each ideal parameter to actual modal parameter have been gained. Finally, three kinds of models: real bridge, ideal model and theory model are established in finite element analysis software ANSYS. Their modal parameters and similarity ratios have been calculated and obtained, which validates above-mentioned relationships of mode parameters and similarity ratios.
(2)According to the procedure of experiment modal analysis, choosing appropriate excitation mode and the sensor and adjusting the system, the paper obtains time signals of every test points using the sampling technique of modal separation excitation and time base variation. And then the paper employs estimation of transfer function in the frequency-domain signals which are converted from FFT. Finally, the paper fits modal parameters of system through the frequency-domain method.
(3)Impulse response function is obtained through the IFFT transformation of the transfer function. And then the modal parameter is calculated through characteristic Economy Realization Arithmetic of time base method (ERA), which is compared with the modal frequency obtained from the method of frequency domain. The MAC is used to validate vibration mode of model.
(4)Experimental modal analysis of 8 working conditions is conducted: the tension of the cables is changed in order to study the effect of the variation of the cable's tension on the structure mode parameter; The number of the cables is gradually reduced to zero, so as to study the effect of the existence and density of cable on the mode parameters. In addition, according to the effect of the cable on the mode parameters, some suggestions are proposed.
引文
[1] 王莲香,周水兴.马来西亚吉隆坡普特拉贾亚城的斜拉拱组合桥.世界桥梁, 2004,(4):9-12
[2] 罗世东,王新国,王庭正等.大跨径斜拉拱桥创新技术构思与研究.桥梁建设,2005,(6):31-33
[3] Pascal Klein, Michael Yamout. Cable-stsyed arch bridge, Putrajaya, Kuala Lumpur. Structural Engineering International, 2003, (3):196-199
[4] 赵跃宇,康厚军,周海兵.斜拉拱桥结构的建模与静力分析.中南公路工程,2006,31(4):14-18
[5] 赵跃宇,吕建根,易壮鹏.斜拉拱桥的力学性能及经济性能的研究.世界桥梁, 2005,(1):29-32
[6] 赵跃宇,刘伟长,杨相展.大跨径斜拉钢管混凝土拱桥空间稳定性分析.公路, 2006,(8):68-71
[7] 赵跃宇,康厚军,王连华等.索-拱结构面内稳定性研究.湖南大学学报,2006, 33(3):1-5
[8] 金波,赵跃宇,冯锐等.横撑对斜拉拱桥稳定性的影响.湖南大学学报:自然科学版,2006,33(6):6-10
[9] 桂婞，罗世东，王新国.大跨径斜拉拱桥结构受力的敏感性分析.桥梁建设,2006,(02):86-89
[10] 杨相展.大跨度斜拉钢管混凝土拱桥动力学及拉索振动研究:[湖南大学硕士学位论文].长沙:湖南大学,2005:36-39
[11] 康厚军.索拱结构的稳定与振动研究:[湖南大学博士学位论文].长沙:湖南大学,2007:135-137
[12] 傅志方,华宏星.模态分析理论与应用.上海:上海交通大学出版社,2000:1-5 [ 13 ] Brian J.Schwarz , Mark H.Richardson.Experimental Modal Analysis.CSI: Reliability Week,1999:7-10
[14] 顾培英,邓昌,吴福生.结构模态分析及其损失诊断.南京:东南大学出版社,2008:2-4
[15] 管迪华.模态分析技术.北京:清华大学出版社,1996:4-6
[16] 张令弥.结构动力学中的几种识别模态识别方法.工程振动与控制,1981,11(2):23-27
[17] A.F. Seykert.Estimation of damping from response spectra.Journal of Sound and Vibration,1981,75(2):199-206 [ 18 ] Peter Avitabile.Experimental Modal Analysis—A simple Non-Mathematical Presentation.Sound and Vibration,2001,(1):1-11
[19] 李德葆,陆秋海.试验模态分析及应用.北京:科学出版社,2001:92-102
[20] 周传荣,赵淳生.机械振动参数识别及其应用.北京:科学出版社,1989:3-8
[21] J.H.金斯伯格.机械与结构振动理论与应用. 北京:中国宇航出版社,2005:26-32
[22] Guid De Roeck et al.Benchmark study on system identification through ambient vibration measurements. IMAC, 2000,(18):1106-1112
[23] Rune Brincker et al. Modal identification from ambient responses using frequency domain decomposition. IMAC, 2000,(18):625-630 [ 24 ] Ibrahim S R.Random decrement technique for modal identification of structures.Journal of Spacedraft and Rockets, 1977, 14(11):696-700 [ 25 ] M.Mergeay.Least squares complex exponential method and globalsystem parameter estimation usde by modal analysis. Proc.of the 5th International Weminar on Modal Analysis,1983,(5):34-39
[26] Leuriem J M,Vold H.A Time Domain Linear Modal Estimation Technique for Global Modal Parameter Identification. Proc.of the 2nd IMAC,1984,(2):12-18
[27] Juang J N,Pappa R S.An eigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance,1985,8(5):620-627
[28] Box G E P,Jenkins G M.Time Series Analysis,Forecasting and Control.San Francisco:Holden-Day,1976:25-36
[29] 曾庆华,张令弥,张春宁.飞行颤振试验数据处理方法及软件研制.航空学报,1994,15(12):76-79
[30] 刘福强,张令弥.一种改进的特征系统实现算法及其在智能结构中的应用. 振动工程学报,1999,12(3):316-322
[31] 徐丽.基于模态参数的混凝土框架结构损伤诊断研究:[湖南大学博士学位论文].长沙:湖南大学,2004:38-68
[32] 庞世伟,于开平,邹经湘. 识别时变结构模态参数的改进子空间方法.应用力学学报,2005,22(2):184-188
[33] N.E.Huang,Z.Shen,S.Long et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc.R.Soc.A,1998,(454):903-995
[34] A.N.Robertson,K.C.Park and K.F.Alvin. Extraction of impulse response data via wavelet transform for structural identification. ASME Journal of Vibration and Acoustics,1998,120(1):252-260
[35] 谭冬梅,姚三,瞿伟廉.振动模态的参数识别综述.华中科技大学学报,2002,19(3):73-78
[36] 沃德.海伦等.模态分析理论与试验(白化同,郭继忠译).北京:北京理工大学出版社,2001:28-31
[37] 赵跃宇等.湘潭市湘江四桥主桥整体模型试验报告.长沙:湖南大学土木工程学院,2005:6-21
[38] 徐挺.相似理论与模型试验.北京:中国农业机械出版社,1982:19-25
[39] 李德寅,王邦楣,林亚超.结构模型试验.北京:科学出版社,1996:56-60
[40] 陈常松,颜东煌,陈政清.岳阳洞庭湖大桥模型动力特性分析.中外公路,2002,22(6):66-69
[41] K.J.巴斯.工程分析中的有限元法.北京:机械工业出版社,1991:90-96
[42] 徐建等.建筑振动工程手册.北京:中国建筑工业出版社,2002:3-9
[43] 应怀樵.脉冲力与结构振动响应传递函数的变时基、变窗长采样分析新方法研究.北京:中国国家发明专利, 1990:23-26
[44] 张令弥, 刘福强.大跨径斜拉桥相似模型结构动态特性试验的分离模态法.振动、测试与诊断,1999,(19):128-132
[45] 曹树谦,张文德,萧龙翔.振动结构模态分析.天津:天津大学出版社,2001:104-116
[46] 王文涛.斜拉桥换索工程.北京:人民交通出版社,1997:112-114
[47] 陈政清.桥梁风工程.北京:人民交通出版社,2005:86-92
[48] 邵旭东.桥梁工程.北京:人民交通出版社,2004:401-402
[49] 赵翔.拉索损伤对斜拉桥结构性能影响的研究:[东南大学博士学位论文].南京:东南大学,2005:85-96
[50] 刘效尧,蔡键,刘晖.桥梁损伤诊断.北京:人民交通出版社,2002:111-119
[2] 罗世东,王新国,王庭正等.大跨径斜拉拱桥创新技术构思与研究.桥梁建设,2005,(6):31-33
[3] Pascal Klein, Michael Yamout. Cable-stsyed arch bridge, Putrajaya, Kuala Lumpur. Structural Engineering International, 2003, (3):196-199
[4] 赵跃宇,康厚军,周海兵.斜拉拱桥结构的建模与静力分析.中南公路工程,2006,31(4):14-18
[5] 赵跃宇,吕建根,易壮鹏.斜拉拱桥的力学性能及经济性能的研究.世界桥梁, 2005,(1):29-32
[6] 赵跃宇,刘伟长,杨相展.大跨径斜拉钢管混凝土拱桥空间稳定性分析.公路, 2006,(8):68-71
[7] 赵跃宇,康厚军,王连华等.索-拱结构面内稳定性研究.湖南大学学报,2006, 33(3):1-5
[8] 金波,赵跃宇,冯锐等.横撑对斜拉拱桥稳定性的影响.湖南大学学报:自然科学版,2006,33(6):6-10
[9] 桂婞，罗世东，王新国.大跨径斜拉拱桥结构受力的敏感性分析.桥梁建设,2006,(02):86-89
[10] 杨相展.大跨度斜拉钢管混凝土拱桥动力学及拉索振动研究:[湖南大学硕士学位论文].长沙:湖南大学,2005:36-39
[11] 康厚军.索拱结构的稳定与振动研究:[湖南大学博士学位论文].长沙:湖南大学,2007:135-137
[12] 傅志方,华宏星.模态分析理论与应用.上海:上海交通大学出版社,2000:1-5 [ 13 ] Brian J.Schwarz , Mark H.Richardson.Experimental Modal Analysis.CSI: Reliability Week,1999:7-10
[14] 顾培英,邓昌,吴福生.结构模态分析及其损失诊断.南京:东南大学出版社,2008:2-4
[15] 管迪华.模态分析技术.北京:清华大学出版社,1996:4-6
[16] 张令弥.结构动力学中的几种识别模态识别方法.工程振动与控制,1981,11(2):23-27
[17] A.F. Seykert.Estimation of damping from response spectra.Journal of Sound and Vibration,1981,75(2):199-206 [ 18 ] Peter Avitabile.Experimental Modal Analysis—A simple Non-Mathematical Presentation.Sound and Vibration,2001,(1):1-11
[19] 李德葆,陆秋海.试验模态分析及应用.北京:科学出版社,2001:92-102
[20] 周传荣,赵淳生.机械振动参数识别及其应用.北京:科学出版社,1989:3-8
[21] J.H.金斯伯格.机械与结构振动理论与应用. 北京:中国宇航出版社,2005:26-32
[22] Guid De Roeck et al.Benchmark study on system identification through ambient vibration measurements. IMAC, 2000,(18):1106-1112
[23] Rune Brincker et al. Modal identification from ambient responses using frequency domain decomposition. IMAC, 2000,(18):625-630 [ 24 ] Ibrahim S R.Random decrement technique for modal identification of structures.Journal of Spacedraft and Rockets, 1977, 14(11):696-700 [ 25 ] M.Mergeay.Least squares complex exponential method and globalsystem parameter estimation usde by modal analysis. Proc.of the 5th International Weminar on Modal Analysis,1983,(5):34-39
[26] Leuriem J M,Vold H.A Time Domain Linear Modal Estimation Technique for Global Modal Parameter Identification. Proc.of the 2nd IMAC,1984,(2):12-18
[27] Juang J N,Pappa R S.An eigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance,1985,8(5):620-627
[28] Box G E P,Jenkins G M.Time Series Analysis,Forecasting and Control.San Francisco:Holden-Day,1976:25-36
[29] 曾庆华,张令弥,张春宁.飞行颤振试验数据处理方法及软件研制.航空学报,1994,15(12):76-79
[30] 刘福强,张令弥.一种改进的特征系统实现算法及其在智能结构中的应用. 振动工程学报,1999,12(3):316-322
[31] 徐丽.基于模态参数的混凝土框架结构损伤诊断研究:[湖南大学博士学位论文].长沙:湖南大学,2004:38-68
[32] 庞世伟,于开平,邹经湘. 识别时变结构模态参数的改进子空间方法.应用力学学报,2005,22(2):184-188
[33] N.E.Huang,Z.Shen,S.Long et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc.R.Soc.A,1998,(454):903-995
[34] A.N.Robertson,K.C.Park and K.F.Alvin. Extraction of impulse response data via wavelet transform for structural identification. ASME Journal of Vibration and Acoustics,1998,120(1):252-260
[35] 谭冬梅,姚三,瞿伟廉.振动模态的参数识别综述.华中科技大学学报,2002,19(3):73-78
[36] 沃德.海伦等.模态分析理论与试验(白化同,郭继忠译).北京:北京理工大学出版社,2001:28-31
[37] 赵跃宇等.湘潭市湘江四桥主桥整体模型试验报告.长沙:湖南大学土木工程学院,2005:6-21
[38] 徐挺.相似理论与模型试验.北京:中国农业机械出版社,1982:19-25
[39] 李德寅,王邦楣,林亚超.结构模型试验.北京:科学出版社,1996:56-60
[40] 陈常松,颜东煌,陈政清.岳阳洞庭湖大桥模型动力特性分析.中外公路,2002,22(6):66-69
[41] K.J.巴斯.工程分析中的有限元法.北京:机械工业出版社,1991:90-96
[42] 徐建等.建筑振动工程手册.北京:中国建筑工业出版社,2002:3-9
[43] 应怀樵.脉冲力与结构振动响应传递函数的变时基、变窗长采样分析新方法研究.北京:中国国家发明专利, 1990:23-26
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