多点激励下结构随机地震反应分析的反应谱方法
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摘要
基于随机振动理论,提出了多点激励作用下线性系统随机地震反应分析的均值反应谱方法,给出了结构峰值反应的均值、标准差以及反应平均频率的反应谱组合公式。这可以将反应谱方法推广应用到多点激励结构的抗震可靠度分析中。鉴于组合公式中谱参数和相关系数需要由烦琐的数值积分得到,本文进一步针对它们给出合理的简化计算式,从而使得建议的反应谱方法的计算效率大大增加。最后,以一个双塔斜拉桥为例,对本文方法进行了验证。基于建议方法的计算结果与MonteCarlo模拟结果吻合较好。与经典的多点激励反应谱方法(MSRS法)比较,本文方法具有其无法比拟的计算效率。
Based on the random vibration theory, a response spectrum method for random vibration analysis of linear, multi-degree-of-freedom structures under multi-support excitations is developed. Various response quantities, including the mean and variance of the peak response, the response mean frequency, are obtained from proposed combination rules in terms of the mean response spectrum. This method makes it possible to apply the response spectrum to the seismic reliability analysis of structures subjected to multi-support excitations. Considering that numerical integration is required to compute the spectral parameters and correlation coefficients in above combination rules, this paper further offers a simplified procedure for their computation, which greatly enhances the computational efficiency of the method suggested in this paper. In the end, the proposed method is demonstrated for a (double)-tower cable-stayed bridge under multi-support excitations. Computed results based on the response spectrum method are in good agreement with Monte Carlo simulation results. And compared to the MSRS method, a well-(developed) multi-support response spectrum method, the proposed method has incomparable computational efficiency.
Based on the random vibration theory, a response spectrum method for random vibration analysis of linear, multi-degree-of-freedom structures under multi-support excitations is developed. Various response quantities, including the mean and variance of the peak response, the response mean frequency, are obtained from proposed combination rules in terms of the mean response spectrum. This method makes it possible to apply the response spectrum to the seismic reliability analysis of structures subjected to multi-support excitations. Considering that numerical integration is required to compute the spectral parameters and correlation coefficients in above combination rules, this paper further offers a simplified procedure for their computation, which greatly enhances the computational efficiency of the method suggested in this paper. In the end, the proposed method is demonstrated for a (double)-tower cable-stayed bridge under multi-support excitations. Computed results based on the response spectrum method are in good agreement with Monte Carlo simulation results. And compared to the MSRS method, a well-(developed) multi-support response spectrum method, the proposed method has incomparable computational efficiency.
引文
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[12] DavenportAG.Noteonthedistributionofthelargestvalueofarandomfunctionwithapplicationtogustloading[A].ProceedingsInstitutionofCivilEngineers[C].London,1964.28:187～196.
[13] DerKiureghianA.Structuralresponsetostationaryexcitation[J].J.EngngMech.,1980,106:1195～1213.
[14] HarichandranRS.Spatialvariationofearthquakegroundmotion[R].MichiganStateUniversity,EastLansing,MI,1999.
[15] LohCH.AnalysisofthespatialvariationofseismicwavesandgroundmovementsfromSMART-1arraydata[J].EarthquakeEngngStruct.Dyn.,1985,14:561～581.
[16] 王君杰,范立础.规范反应谱长周期部分修正方法的探讨[J].土木工程学报,1998,31(6):49～55.
[17] HaoH,OliveraCS,PenzienJ.Multiple stationgroundmotionprocessingandsimulationbasedonSMART 1arraydata[J].Nucl.EngngDesign,1989,111:293～310.
[18] 李建华,李杰.考虑反应谱变异性的人工合成地震波[J].同济大学学报,2002,30(9):1038～1043.
[2] BerrahM,KauselE.Responsespectrumanalysisofstructuressubjectedtospatiallyvaryingmotions[J].EarthquakeEngngStruct.Dyn.,1992,21:461～470.
[3] BerrahM,KauselE.Amodalcombinationruleforspatiallyvaryingseismicmotions[J].EarthquakeEngngStruct.Dyn.,1993,22:791～800.
[4] Heredia ZavoniE,VanmarckeEH.Seismicrandom vibrationanalysisofmultisupport structuralsystems[J].J.EngngMech.,1994,120(5):1107～1128.
[5] CloughR,PenzienJ.Dynamicsofstructures[M].NewYork:McGraw HillBookCo.1993.
[6] 李杰,李国强.地震工程学导论[M].地震出版社,北京:1992.
[7] Vanmarcke,EH.Propertiesofspectralmomentswithapplicationstorandomvibration[J].J.Engrg.Mech.,1972,198:425～446.
[8] HaoH.Archresponsetocorrelatedmultipleexcitations.EarthquakeEngngStruct.Dyn.,1993,22:389～404.
[9] NakmuraY,DerKiureghianA,LiuD.Multiple supportresponsespectrumanalysisofthegoldengatebridge[R].ReportNo.UCB/EERC 93/05,EERC,UniversityofCalifornia,Berkeley,CA,1993.
[10] 王君杰,王前信,江近仁.大跨度拱桥在空间变化地震动下的响应[J].振动工程学报,1995,8(2):119～126.
[11] HarichandranRS,HawwariA,SweidanBN.Responseoflong spanbridgestospatiallyvaryinggroundmotion[J].Struct.Engng,1996,122(5):476～484.
[12] DavenportAG.Noteonthedistributionofthelargestvalueofarandomfunctionwithapplicationtogustloading[A].ProceedingsInstitutionofCivilEngineers[C].London,1964.28:187～196.
[13] DerKiureghianA.Structuralresponsetostationaryexcitation[J].J.EngngMech.,1980,106:1195～1213.
[14] HarichandranRS.Spatialvariationofearthquakegroundmotion[R].MichiganStateUniversity,EastLansing,MI,1999.
[15] LohCH.AnalysisofthespatialvariationofseismicwavesandgroundmovementsfromSMART-1arraydata[J].EarthquakeEngngStruct.Dyn.,1985,14:561～581.
[16] 王君杰,范立础.规范反应谱长周期部分修正方法的探讨[J].土木工程学报,1998,31(6):49～55.
[17] HaoH,OliveraCS,PenzienJ.Multiple stationgroundmotionprocessingandsimulationbasedonSMART 1arraydata[J].Nucl.EngngDesign,1989,111:293～310.
[18] 李建华,李杰.考虑反应谱变异性的人工合成地震波[J].同济大学学报,2002,30(9):1038～1043.
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