基于模态参数的梁桥结构模型边界条件参数修正
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摘要
针对实际桥梁结构复杂的边界条件,详细分析边界条件的附加约束参数。以梁桥结构的水平平动附加约束与扭转附加约束参数为讨论对象,采用最小二乘约束优化反演理论,建立以模态参数实测值与理论计算值误差平方和最小为目标的桥梁结构边界条件变异参数约束优化反演求解问题。在其基础上引入矩阵摄动理论,将结构动力方程的特征值及特征向量一阶摄动代入所建立约束优化方程,显著提高优化求解效率,并通过迭代求解的方式提高边界条件变异参数的求解精度。编制相应求解程序,通过某磁浮轨道梁方案的损伤识别验证表明,仅用前几阶仿真计算得到的模拟实测频率与振型经过4次迭代即可精确反演桥梁结构边界条件变异参数。
In view of the complex boundary conditions of real bridge structures,the appendix restrain parameters of structure boundary contitions were analyzed in detail.The appendix horizontal and torsional restrain parameters were selected as the research objects.The least square constrained optimization inversion method was used to establish the question of reverse of bridge structure boundary appendix parameters based on tested and calculated mode parameters.On the basis of the matrix perturbation theory,the first order eigen-value and eigen-vector were substituted into the constrained optimization inversion equation,so the solving efficiency was improved greatly,and the iteration method was used to improve the precision.The corresponding solving program was made.The example of a maglev railway girder shows that fairly good precise bridge structure boundary appendix parameters can be reserved with only several former calculated mode parameters through four times of iteration calculation.
In view of the complex boundary conditions of real bridge structures,the appendix restrain parameters of structure boundary contitions were analyzed in detail.The appendix horizontal and torsional restrain parameters were selected as the research objects.The least square constrained optimization inversion method was used to establish the question of reverse of bridge structure boundary appendix parameters based on tested and calculated mode parameters.On the basis of the matrix perturbation theory,the first order eigen-value and eigen-vector were substituted into the constrained optimization inversion equation,so the solving efficiency was improved greatly,and the iteration method was used to improve the precision.The corresponding solving program was made.The example of a maglev railway girder shows that fairly good precise bridge structure boundary appendix parameters can be reserved with only several former calculated mode parameters through four times of iteration calculation.
引文
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[12]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].成都:西南交通大学,2005.
[13]Pelin Gundes Bakir,Edwin Reynders,Guido DeRoeck.Sensitivity-based Finite Element Model Upda-ting Using Constrained Optimization with a Trust Re-gion Algorithm[J].Journal of Sound and Vibration,2007,305(1-2):211-225.
[2]施洲.基于动力测试的桥梁结构损伤识别及性能评定理论与应用研究[D].成都:西南交通大学,2007.
[3]Shuncong Zhong,S.Olutunde Oyadiji,Kang Ding.Response-onlyMethod for Damage Detection of Beam-like Structures UsingHigh Accuracy Frequencies with Auxiliary Mass Spatial Probing[J].Journal of Sound and Vibration,2008,311(3-5):1075-1099.
[4]Nam-Gyu Park,Youn-Sik Park.Damage Detection UsingSpatially Incomplete Frequency Response Functions[J].Mechanical Systems and Signal Processing,2003,17(3):519-532.
[5]Zhang Q W.Statistical Damage Identification for BridgesUsing Ambient Vibration data[J].Computers&Struc-tures,2007,85(7-8):476-485.
[6]庄军生.桥梁支座[M].2版.北京:中国铁道出版社,2002.
[7]LEE S Y,KE H Y.Free Vibration of a Nonuniform Beamwith General Elastically Restrained Boundary Conditions[J].Journal of Sound and Vibration,1990.136(3):425-437.
[8]刘玉明,易伟建.一种识别结构系统边界条件的新方法[J].湖南大学学报:自然科学版,1999.(4):99-107.LIU Yu-ming,YI Wei-jian.A New Method for Identifyingthe Boundary Condition of Structural System[J].Journal ofHunan University:Natural Sciences Edition,1999.(4):99-107.
[9]姜海波,赵人达.带边界条件损伤简支梁振动模态分析[J].振动与冲击,2004,23(2):72-77.JIANG Hai-bo,ZHAO Ren-da.Vibration Node Analysis ofSimply Supported Beam with Damage Boundary Condition[J].Journal of Vibration and Shock,2004,23(2):72-77.
[10]施洲,赵人达.桥梁结构边界条件变异对固有振动特性的影响分析[J].地震工程与工程振动,2007,27(5):117-123.SHI Zhou,ZHAO Ren-da.Analysis of Changes of theBoundary Conditions on Effects of Free-vibration Charac-teristic of Bridge Structure[J].Journal of Vibration andShock,2007,27(5):117-123.
[11]黄光远,刘小军.数学物理反问题[M].济南:山东科学技术出版社,1993.
[12]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].成都:西南交通大学,2005.
[13]Pelin Gundes Bakir,Edwin Reynders,Guido DeRoeck.Sensitivity-based Finite Element Model Upda-ting Using Constrained Optimization with a Trust Re-gion Algorithm[J].Journal of Sound and Vibration,2007,305(1-2):211-225.
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