大跨度空间结构抗震分析的非平稳随机振动时域显式法
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摘要
大跨度空间结构自振频率高度密集,振型耦联作用明显,采用传统振型分解反应谱法计算结构地震响应时,存在振型组合数量大、组合方式不尽合理等问题。采用真正意义的随机振动方法计算大型复杂结构地震响应的需求越来越迫切。时域显式法基于动力响应显式表达式进行随机振动分析,具有良好的计算精度和计算效率,为大型复杂结构的随机振动分析提供了一条有效途径。以时域显式法为基础,在通用有限元软件平台上实现了大跨度空间结构在非平稳地震作用下的随机响应分析。以广州亚运会自行车馆抗震分析为工程应用实例,验证了时域显式法在大跨度空间结构抗震分析中的高效性;同时,计算结果还表明,相对于时域显式法的结果,传统反应谱法的计算结果偏于保守。
The natural frequencies of large-span spatial structures are usually closely spaced,and the corresponding mode shapes are always highly coupled.A large number of mode shapes and a more reasonable combination rule between different modes are required when using the conventional response spectrum method(RSM) for seismic analysis of such structures.It is therefore in great demand to conduct seismic analysis of large complex structures by a real random vibration method.Based on the explicit expressions of dynamic responses,the time-domain explicit method(TDEM) has a good computational accuracy and efficiency for random vibration analysis.It offers an effective way for random vibration analysis of large and complex structures.Based on the framework of TDEM,random response analysis of large-span spatial structures subjected to non-stationary seismic excitations is accomplished by utilizing commercial finite element programs.Seismic analysis of the Guangzhou Cycling Gymnasium is conducted by TDEM,indicating the high efficiency of the present method.The results of TDEM are also compared with those obtained by RSM,showing that the latter tend to be conservative.
The natural frequencies of large-span spatial structures are usually closely spaced,and the corresponding mode shapes are always highly coupled.A large number of mode shapes and a more reasonable combination rule between different modes are required when using the conventional response spectrum method(RSM) for seismic analysis of such structures.It is therefore in great demand to conduct seismic analysis of large complex structures by a real random vibration method.Based on the explicit expressions of dynamic responses,the time-domain explicit method(TDEM) has a good computational accuracy and efficiency for random vibration analysis.It offers an effective way for random vibration analysis of large and complex structures.Based on the framework of TDEM,random response analysis of large-span spatial structures subjected to non-stationary seismic excitations is accomplished by utilizing commercial finite element programs.Seismic analysis of the Guangzhou Cycling Gymnasium is conducted by TDEM,indicating the high efficiency of the present method.The results of TDEM are also compared with those obtained by RSM,showing that the latter tend to be conservative.
引文
[1]GB 50011—2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.(GB 50011—2010 Codefor seismic design of buildings[S].Beijing:ChinaArchitecture&Building Press,2010.(in Chinese))
[2]Subbaraj K,Dokainish M A.A survey of direct timeintegration methods in computational structuraldynamic:I:explicit methods,implicit methods[J].Computers and Structures,1989,32(6):1371-1386.
[3]Newmark N M.A method of computation for structuraldynamics[J].Journal of Engineering Mechanics,1959,85(3):67-94.
[4]Bathe K J,Wilson E L.Numerical methods in finiteelement analysis[M].New Jersey:Prentice-Hall,1976:308-344.
[5]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:42-80.(LIN Jiahao,ZHANGYahui.Pseudo-excitation method of random vibration[M].Beijing:Science Press,2004:42-80.(inChinese))
[6]BS EN 1998-2:2005 Eurocode 8:design ofstructures for earthquake resistance:part 2:bridges[S].London:BSI,2005.
[7]JTG/TB 02-01—2008公路桥梁抗震细则[S].北京:人民交通出版社,2008.(JTG/TB 02-01—2008Guidelines for seismic design of highway bridges[S].Beijing:People’s Communications Press,2008.(inChinese))
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[9]苏成,徐瑞.非平稳随机激励下结构体系动力可靠度时域解法[J].力学学报,2010,42(3):512-520.(SU Cheng,XU Rui.Time-domain numericalsimulation method for dynamic reliability of structuralsystems subjected to non-stationary random excitations[J].Chinese Journal of Theoretical and AppliedMechanics,2010,42(3):512-520.(in Chinese))
[10]苏成,徐瑞.非平稳地震作用下随机结构动力可靠度计算[J].振动工程学报,2011,24(2):118-124.(SUCheng,XU Rui.Dynamic reliability analysis ofstochastic structures subjected to non-stationary seismicexcitations[J].Journal of Vibration Engineering,2011,24(2):118-124.(in Chinese))
[11]Su Cheng,Xu Rui.Time domain method for randomvibration analysis of structures subjected to non-stationary seismic excitation[J].Acta Mechanica SolidaSinica,2010,23(Special Issue):169-174.
[12]徐瑞.大型复杂结构非平稳随机振动分析方法研究[D].广州:华南理工大学,2010.(XU Rui.A study onnon-stationary random vibration analysis for large andcomplex structures[D].Guangzhou:South ChinaUniversity of Technology,2010.(in Chinese))
[13]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.(ZHONGWanxie.On precise time-integration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131-136.(in Chinese))
[14]Davenport A G.Note on the distribution of the largestvalue of a random function with application to gustloading[J].Proceedings of Institution of CivilEngineers,1964,28(2):187-196.
[15]Kiureghian A D.Structural response to stationaryrandom excitation[J].Journal of EngineeringMechanics,1980,106(6):1195-1213.
[16]Yang J N,Liu S C.Statistical interpretation andapplication of response spectra[C]//Proceedings of7th WCEE.Istanbul:The Turkish National Committeeon Earthquake Engineering,1980,6:657-663
[17]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-11.(JIANGJinren,HONG Feng.Conversion between powerspectrum and response spectrum and artificialearthquakes[J].Earthquake Engineering andEngineering Vibration,1984,4(3):1-11.(inChinese))
[18]赵凤新,刘爱文.地震动功率谱与反应谱的转换关系[J].地震工程与工程振动,2001,21(2):30-35.(ZHAO Fengxin,LIU Aiwen.Relationship betweenpower spectral-density functions and response spectra ofearthquake ground motions[J].Earthquake Engineeringand Engineering Vibration,2001,21(2):30-35.(inChinese))
[19]Shrikhande M,Gupta V K.求解结构体系地震反应的普遍化方法[J].世界地震工程,1998,14(2):78-85.(Shrikhande M,Gupta V K.A generalized approach forthe seismic response of structural systems[J].WorldInformation on Earthquake Engineering,1998,14(2):78-85.(in Chinese))
[20]张治勇,孙柏涛,宋天舒.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,2000,16(3):33-38.(ZHANG Zhiyong,SUN Baitao,SONGTianshu.Study on the parameters of seismic powerspectrum model based on the new seismic code[J].World Information on Earthquake Engineering,2000,16(3):33-38.(in Chinese))
[21]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10.(Xue Suduo,Wang Xuesheng,Cao Zi.Parametersstudy on seismic random model based on the newseismic code[J].China Civil Engineering Journal,2003,36(5):5-10.(in Chinese))
[22]GBJ 11—1989建筑抗震设计规范[S].北京:中国建筑工业出版社,1989.(GBJ 11—1989 Code forseimic design of buildings[S].Beijing:ChinaArchitecture&Building Press,1989.(in Chinese))
[23]GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.(GB 50011—2001 Codefor seismic design of buildings[S].Beijing:ChinaArchitecture&Building Press,2001.(in Chinese))
[24]Shinozuka M.Simulation of multivariate andmultidimensional random processes[J].Journal of theAcoustical Society of America,1971,49(1):357-368.
[2]Subbaraj K,Dokainish M A.A survey of direct timeintegration methods in computational structuraldynamic:I:explicit methods,implicit methods[J].Computers and Structures,1989,32(6):1371-1386.
[3]Newmark N M.A method of computation for structuraldynamics[J].Journal of Engineering Mechanics,1959,85(3):67-94.
[4]Bathe K J,Wilson E L.Numerical methods in finiteelement analysis[M].New Jersey:Prentice-Hall,1976:308-344.
[5]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:42-80.(LIN Jiahao,ZHANGYahui.Pseudo-excitation method of random vibration[M].Beijing:Science Press,2004:42-80.(inChinese))
[6]BS EN 1998-2:2005 Eurocode 8:design ofstructures for earthquake resistance:part 2:bridges[S].London:BSI,2005.
[7]JTG/TB 02-01—2008公路桥梁抗震细则[S].北京:人民交通出版社,2008.(JTG/TB 02-01—2008Guidelines for seismic design of highway bridges[S].Beijing:People’s Communications Press,2008.(inChinese))
[8]苏成,徐瑞.非平稳激励下结构随机振动时域分析法[J].工程力学,2010,27(12):77-83.(SU Cheng,XURui.Random vibration analysis of structures subjectedto non-stationary excitations by time domain method[J].Engineering Mechanics,2010,27(12):77-83.(in Chinese))
[9]苏成,徐瑞.非平稳随机激励下结构体系动力可靠度时域解法[J].力学学报,2010,42(3):512-520.(SU Cheng,XU Rui.Time-domain numericalsimulation method for dynamic reliability of structuralsystems subjected to non-stationary random excitations[J].Chinese Journal of Theoretical and AppliedMechanics,2010,42(3):512-520.(in Chinese))
[10]苏成,徐瑞.非平稳地震作用下随机结构动力可靠度计算[J].振动工程学报,2011,24(2):118-124.(SUCheng,XU Rui.Dynamic reliability analysis ofstochastic structures subjected to non-stationary seismicexcitations[J].Journal of Vibration Engineering,2011,24(2):118-124.(in Chinese))
[11]Su Cheng,Xu Rui.Time domain method for randomvibration analysis of structures subjected to non-stationary seismic excitation[J].Acta Mechanica SolidaSinica,2010,23(Special Issue):169-174.
[12]徐瑞.大型复杂结构非平稳随机振动分析方法研究[D].广州:华南理工大学,2010.(XU Rui.A study onnon-stationary random vibration analysis for large andcomplex structures[D].Guangzhou:South ChinaUniversity of Technology,2010.(in Chinese))
[13]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.(ZHONGWanxie.On precise time-integration method forstructural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131-136.(in Chinese))
[14]Davenport A G.Note on the distribution of the largestvalue of a random function with application to gustloading[J].Proceedings of Institution of CivilEngineers,1964,28(2):187-196.
[15]Kiureghian A D.Structural response to stationaryrandom excitation[J].Journal of EngineeringMechanics,1980,106(6):1195-1213.
[16]Yang J N,Liu S C.Statistical interpretation andapplication of response spectra[C]//Proceedings of7th WCEE.Istanbul:The Turkish National Committeeon Earthquake Engineering,1980,6:657-663
[17]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-11.(JIANGJinren,HONG Feng.Conversion between powerspectrum and response spectrum and artificialearthquakes[J].Earthquake Engineering andEngineering Vibration,1984,4(3):1-11.(inChinese))
[18]赵凤新,刘爱文.地震动功率谱与反应谱的转换关系[J].地震工程与工程振动,2001,21(2):30-35.(ZHAO Fengxin,LIU Aiwen.Relationship betweenpower spectral-density functions and response spectra ofearthquake ground motions[J].Earthquake Engineeringand Engineering Vibration,2001,21(2):30-35.(inChinese))
[19]Shrikhande M,Gupta V K.求解结构体系地震反应的普遍化方法[J].世界地震工程,1998,14(2):78-85.(Shrikhande M,Gupta V K.A generalized approach forthe seismic response of structural systems[J].WorldInformation on Earthquake Engineering,1998,14(2):78-85.(in Chinese))
[20]张治勇,孙柏涛,宋天舒.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,2000,16(3):33-38.(ZHANG Zhiyong,SUN Baitao,SONGTianshu.Study on the parameters of seismic powerspectrum model based on the new seismic code[J].World Information on Earthquake Engineering,2000,16(3):33-38.(in Chinese))
[21]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10.(Xue Suduo,Wang Xuesheng,Cao Zi.Parametersstudy on seismic random model based on the newseismic code[J].China Civil Engineering Journal,2003,36(5):5-10.(in Chinese))
[22]GBJ 11—1989建筑抗震设计规范[S].北京:中国建筑工业出版社,1989.(GBJ 11—1989 Code forseimic design of buildings[S].Beijing:ChinaArchitecture&Building Press,1989.(in Chinese))
[23]GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.(GB 50011—2001 Codefor seismic design of buildings[S].Beijing:ChinaArchitecture&Building Press,2001.(in Chinese))
[24]Shinozuka M.Simulation of multivariate andmultidimensional random processes[J].Journal of theAcoustical Society of America,1971,49(1):357-368.
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