一种计算地震作用下相邻结构相对位移的改进差异谱方法
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摘要
作为当前铁路客站建设中经常采用的一种结构形式,"房桥分离"结构在地震激励下存在客站建筑与桥梁结构发生碰撞的隐患,而规范中缺少对于此类结构形式最小安全间距的相关规定。基于此,作者根据客站建筑与桥梁结构的结构形式,并考虑客站建筑的非比例阻尼特征,通过引入虚拟激励法,推导用于碰撞分析的随机表达式,该计算表达式可以实现准确高效的随机运算。在此基础之上,作者进一步提出一种改进差异谱方法,该反应谱组合公式可用于计算地震作用下相邻结构的相对位移,从而提供避免房桥结构震致碰撞的最小安全间距,相比传统方法其可以考虑建筑物非比例阻尼特征,具备坚实理论基础,形式简洁方便,适于工程应用。最后通过数值算例验证本文所提出改进差异谱方法的准确性和有效性。
As an often adopted structural style in current railway station constructions,the separated structure-bridge station under earthquake excitation involves risks of collision between the station and the elevated bridge,meanwhile,there are not corresponding regulations about the safety spacing in the seismic code.Thereby,according to structural style and dynamic properties of the separated structure-bridge station,a stochastic expression for pounding analysis based on the pseudo-excitation method is proposed,and it takes into account of the non-proportional damping characteristics.Accordingly,the spectral difference method is improved for calculating the relative displacement of adjacent buildings in earthquake and thus providing the minimum spacing between the structure and the elevated bridge for avoiding pounding due to earthquakes.Comparing with the conventional method,the improved spectral difference method can explain the non-proportional damping characteristics with solid theoretical foundation and simplicity.Finally,numerical analysis is carried out to verify the spectral difference method.
As an often adopted structural style in current railway station constructions,the separated structure-bridge station under earthquake excitation involves risks of collision between the station and the elevated bridge,meanwhile,there are not corresponding regulations about the safety spacing in the seismic code.Thereby,according to structural style and dynamic properties of the separated structure-bridge station,a stochastic expression for pounding analysis based on the pseudo-excitation method is proposed,and it takes into account of the non-proportional damping characteristics.Accordingly,the spectral difference method is improved for calculating the relative displacement of adjacent buildings in earthquake and thus providing the minimum spacing between the structure and the elevated bridge for avoiding pounding due to earthquakes.Comparing with the conventional method,the improved spectral difference method can explain the non-proportional damping characteristics with solid theoretical foundation and simplicity.Finally,numerical analysis is carried out to verify the spectral difference method.
引文
[1]李茂生.建桥一体化车站结构研究及其应用[D].上海:同济大学,2007(Li Maosheng.Research on theapplication of the structure of the station integrating bridgewith building[D].Shanghai:Tongji University,2007(inChinese))
[2]Jeng V,Kasai K,Maison B F.A spectral difference methodto estimate building separations to avoid pounding[J].Earthquake Spectra,1992,8(2):201-223
[3]李忠献,岳福青,周莉,等.基于随机振动理论确定桥梁地震碰撞的临界间隙[J].地震工程与工程振动,2006,26(4):156-161(Li Zhongxian,Yue Fuqing,ZhouLi,et al.Determination of critical ga Plength of seismicpounding for bridges based on random vibration theory[J].Earthquake Engineering and Engineering Vibration,2006,26(4):156-161(in Chinese))
[4]Bi K,Hao H,Chouw N.Required separation distance betweendecks and at abutments of a bridge crossing a canyon site toavoid seismic pounding[J].Earthquake Engineering&Structural Dynamics,2010,39(3):303-323
[5]王东升,冯启民,王国新.基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型[J].工程力学,2004,21(2):157-166(Wang Dongsheng,Feng Qimin,WangGuoxin.Analysis model of pounding between adjacentbridge girders during earthquakes based on collinear impactbetween rods[J].Engineering Mechanics,2004,21(2):157-166(in Chinese))
[6]于海龙,朱晞.地震作用下简支梁桥梁间碰撞的反应性能[J].北方交通大学学报,2004,28(1):43-46(YuHailong,Zhu Xi.Characteristic of pounding response ofthe simple-supported bridges during earthquake[J].Journal of Northern Jiaotong University,2004,28(1):43-46(in Chinese))
[7]邓育林,彭天波,李建中.地震作用下桥梁结构横向碰撞模型及参数分析[J].振动与冲击,2007,26(9):104-107,119(Deng Yulin,Peng Tianbo,Li Jianzhong.Pounding model of bridge structures and parameter analysisunder transverse earthquakes[J].Journal of Vibration andShock,2007,26(9):104-107,119(in Chinese))
[8]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133(Li Zhongxian,Yue Fuqing,Zhou Li.Equivalent kelvinimpact model for pounding analysis of bridges duringearthquake[J].Engineering Mechanics,2008,25(4):128-133(in Chinese))
[9]Ye K,Li L,Zhu H.A note on the Hertz contact modelwith nonlinear damping for pounding simulation[J].Earthquake Engineering&Structural Dynamics,2009,38(9):1135-1142
[10]Bhaskararao A V,Jangid R S.Optimum viscous damperfor connecting adjacent SDOF structures for harmonic andstationary white-noise random excitations[J].EarthquakeEngineering&Structural Dynamics,2007,36(4):563-571
[11]Hao H,Shen J.Estimation of relative displacement of twoadjacent asymmetric structures[J].Earthquake Engineering&Structural Dynamics,2001,30(1):81-96
[12]聂利英,李建中,范立础.地震作用下结构碰撞的模型参数及其影响分析[J].工程力学,2005,22(5):142-146(Nie Liying,Li Jianzhong,Fan Lichu.Selection ofpounding analysis parameters and its effects on structureunder earthquake[J].Engineering Mechanics,2005,22(5):142-146(in Chinese))
[13]汪梦甫.非比例阻尼线性体系地震反应计算的振型分解反应谱法[J].地震工程与工程振动,2007,27(1):31-37(Wang Mengfu.On seismic response analysismethods of non-proportional damped linear MDOF systems[J].Journal of Earthquake Engineering and EngineeringVibration,2007,27(1):31-37(in Chinese))
[14]周锡元,俞瑞芳.非比例阻尼线性体系基于规范反应谱的CCQC法[J].工程力学,2006,23(2):10-17(ZhouXiyuan,Yu Ruifang.CCQC method for seismic response ofnon-classically damped linear system based on coderesponse spectra[J].Engineering Mechanics,2006,23(2):10-17(in Chinese))
[15]俞瑞芳.非比例阻尼线性系统随机地震输入下的动力反应分析[D].北京:北京工业大学,2006
[16]Lin J H.A fast CQC algorithm of PSD matrices for randomseismic responses[J].Computers&Structures,1992,44(3):683-687
[2]Jeng V,Kasai K,Maison B F.A spectral difference methodto estimate building separations to avoid pounding[J].Earthquake Spectra,1992,8(2):201-223
[3]李忠献,岳福青,周莉,等.基于随机振动理论确定桥梁地震碰撞的临界间隙[J].地震工程与工程振动,2006,26(4):156-161(Li Zhongxian,Yue Fuqing,ZhouLi,et al.Determination of critical ga Plength of seismicpounding for bridges based on random vibration theory[J].Earthquake Engineering and Engineering Vibration,2006,26(4):156-161(in Chinese))
[4]Bi K,Hao H,Chouw N.Required separation distance betweendecks and at abutments of a bridge crossing a canyon site toavoid seismic pounding[J].Earthquake Engineering&Structural Dynamics,2010,39(3):303-323
[5]王东升,冯启民,王国新.基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型[J].工程力学,2004,21(2):157-166(Wang Dongsheng,Feng Qimin,WangGuoxin.Analysis model of pounding between adjacentbridge girders during earthquakes based on collinear impactbetween rods[J].Engineering Mechanics,2004,21(2):157-166(in Chinese))
[6]于海龙,朱晞.地震作用下简支梁桥梁间碰撞的反应性能[J].北方交通大学学报,2004,28(1):43-46(YuHailong,Zhu Xi.Characteristic of pounding response ofthe simple-supported bridges during earthquake[J].Journal of Northern Jiaotong University,2004,28(1):43-46(in Chinese))
[7]邓育林,彭天波,李建中.地震作用下桥梁结构横向碰撞模型及参数分析[J].振动与冲击,2007,26(9):104-107,119(Deng Yulin,Peng Tianbo,Li Jianzhong.Pounding model of bridge structures and parameter analysisunder transverse earthquakes[J].Journal of Vibration andShock,2007,26(9):104-107,119(in Chinese))
[8]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133(Li Zhongxian,Yue Fuqing,Zhou Li.Equivalent kelvinimpact model for pounding analysis of bridges duringearthquake[J].Engineering Mechanics,2008,25(4):128-133(in Chinese))
[9]Ye K,Li L,Zhu H.A note on the Hertz contact modelwith nonlinear damping for pounding simulation[J].Earthquake Engineering&Structural Dynamics,2009,38(9):1135-1142
[10]Bhaskararao A V,Jangid R S.Optimum viscous damperfor connecting adjacent SDOF structures for harmonic andstationary white-noise random excitations[J].EarthquakeEngineering&Structural Dynamics,2007,36(4):563-571
[11]Hao H,Shen J.Estimation of relative displacement of twoadjacent asymmetric structures[J].Earthquake Engineering&Structural Dynamics,2001,30(1):81-96
[12]聂利英,李建中,范立础.地震作用下结构碰撞的模型参数及其影响分析[J].工程力学,2005,22(5):142-146(Nie Liying,Li Jianzhong,Fan Lichu.Selection ofpounding analysis parameters and its effects on structureunder earthquake[J].Engineering Mechanics,2005,22(5):142-146(in Chinese))
[13]汪梦甫.非比例阻尼线性体系地震反应计算的振型分解反应谱法[J].地震工程与工程振动,2007,27(1):31-37(Wang Mengfu.On seismic response analysismethods of non-proportional damped linear MDOF systems[J].Journal of Earthquake Engineering and EngineeringVibration,2007,27(1):31-37(in Chinese))
[14]周锡元,俞瑞芳.非比例阻尼线性体系基于规范反应谱的CCQC法[J].工程力学,2006,23(2):10-17(ZhouXiyuan,Yu Ruifang.CCQC method for seismic response ofnon-classically damped linear system based on coderesponse spectra[J].Engineering Mechanics,2006,23(2):10-17(in Chinese))
[15]俞瑞芳.非比例阻尼线性系统随机地震输入下的动力反应分析[D].北京:北京工业大学,2006
[16]Lin J H.A fast CQC algorithm of PSD matrices for randomseismic responses[J].Computers&Structures,1992,44(3):683-687
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