考虑空间效应的多支撑管线随机地震响应分析
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摘要
提出了一种能考虑地震动空间变化效应的多支撑管线随机地震响应分析的解析方法.证明了多点地震作用下结构的平稳随机响应分析可转化为求解支座简谐运动时的确定性响应,直接给出了含有待定系数的简谐响应的形式,并通过边界条件和连续性条件建立待定系数的求解方程.与拟静位移分解法相比,该方法不用计算结构的振型以及拟静位移分量,完全是基于解析推导,因此在计算效率方面优势明显.数值算例中,采用该方法和拟静位移分解法计算了一个6跨管线在空间多点地震作用下的随机响应,对比验证了方法的正确性和高效性.
An analytical method was formulated for the random seismic analysis of multi-supported pipelines subjected to spatially varying ground motions. W ith the pseudo-excitation method,the stationary random seismic responses were proven to be represented in terms of deterministic responses of pipelines under multi-support harmonic excitations. The harmonic responses were expressed as a series of harmonic functions with undetermined coefficients,which could be solved with the appropriate boundary and compatibility conditions. In comparison with the quasi-static decomposition method,the present method is derived analytically without computation of the structural normal modes and quasi-static components. The high accuracy and efficiency of the present method is verified through its application to an exemplary 6-span pipeline and the comparison of results made with those from the quasi-static decomposition method.
An analytical method was formulated for the random seismic analysis of multi-supported pipelines subjected to spatially varying ground motions. W ith the pseudo-excitation method,the stationary random seismic responses were proven to be represented in terms of deterministic responses of pipelines under multi-support harmonic excitations. The harmonic responses were expressed as a series of harmonic functions with undetermined coefficients,which could be solved with the appropriate boundary and compatibility conditions. In comparison with the quasi-static decomposition method,the present method is derived analytically without computation of the structural normal modes and quasi-static components. The high accuracy and efficiency of the present method is verified through its application to an exemplary 6-span pipeline and the comparison of results made with those from the quasi-static decomposition method.
引文
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[2]Heredia-Zavoni E,Vanmarcke E H.Seismic random vibration analysis of multi-support structural systems[J].A SC E Journal of Engineering Mechanics,1994,120(5):1107-1128.
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[7]Zhang Y H,Li Q S,Lin J H,Williams F W.Random vibration analysis of long-span structures subjected to spatially varying ground motions[J].Soil D ynamics and Earthquake Engineering,2009,29(4):620-629.
[8]张亚辉,智浩,吕峰.结构多点随机地震响应分析及拟静位移计算[J].计算力学学报,2004,21(5):564-570.(Z HAN G Ya-hui,Z HI Hao,LFeng.Seismic random response analysis of multisupported structures and the quasi-static displacement approximation[J].C hinese Journal of C omputational Mechanics,2004,21(5):564-570.(in C hinese))
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[11]Chen J T,Tsaur D H,Hong H K.An alternative method for transient and random responses of structures subject to support motions[J].Engineering Structures,1997,19(2):162-172.
[12]Lin Y K,Zhang R,Yong Y.Multiply supported pipeline under seismic wave excitations[J].ASCE Journal of Engineering Mechanics,1990,116(5):1094-1108.
[13]Leger P,Ide I M,Paultre P.Multiple-support seismic analysis of large structures[J].Computers&Structures,1990,36(6):1153-1158.
[14]周国良,李小军,刘必灯,齐兴军.大质量法在多点激励分析中的应用,误差分析与改进[J].工程力学,2011,28(1):48-54.(ZHOU Guo-liang,LI Xiao-jun,LIU Bi-deng,QI Xing-jun.Error analysis and improvement of large mass method used in multi-support seismic excitation analysis[J].Engineering Mechanics,2011,28(1):48-54.(in C hinese))
[15]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.(Q U T ie-jun,W AN G Jun-jie,W AN G Q ian-xin.Practical PSD ground motion w ith spatial effect[J].A cta Seismologica Sinica,1996,18(1):55-62.(in C hinese))
[16]冯启民,胡聿贤.空间相关地面运动的数学模型[J].地震工程与工程振动,1981,1(2):1-8.(FENG Qi-min,HU Yu-xian.A mathematical model for spatial seismic ground motion[J].Journal of Earthquake Engineering and Engineering D ynamics,1981,1(2):1-8.(in C hinese))
[17]Loh C H,Yeh Y T.Spatial variation and stochastic modelling of seismic differential ground movement[J].Earthquake Engineering and Structural Dynamics,1988,16(4):583-596.
[18]Der Kiureghian A.A coherency model for spatially varying ground motions[J].Earthquake Engineering and Structural D ynamics,1996,25(1):99-111.
[19]Somerville P G,Mc Laren J P,Sen M K,Helmberger D V.The influence of site conditions on the spatial incoherence of ground motions[J].Structural Safety,1991,10(1):1-13.
[20]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.(LIN Jia-hao,Z HAN G Ya-hui.Pseudo-Excitation Method for R andom V ibration[M].Beijing:Science Press,2004.(in C hinese))
[2]Heredia-Zavoni E,Vanmarcke E H.Seismic random vibration analysis of multi-support structural systems[J].A SC E Journal of Engineering Mechanics,1994,120(5):1107-1128.
[3]Mindlin R D,Goodman L E.Beam vibrations with time-dependent boundary conditions[J].ASME Journal of A pplied Mechanics,1950,17(4):377-380.
[4]Clough R W,Penzien J.Dynamics of Structures[M].New York:Mc Graw-Hill,1993.
[5]Zerva A.Response of multi-span beams to spatially incoherent seismic ground motions[J].Earthquake Engineering and Structural D ynamics,1990,19(6):819-832.
[6]Zerva A.Seismic loads predicted by spatial variability models[J].Structural Safety,1992,11(3):227-243.
[7]Zhang Y H,Li Q S,Lin J H,Williams F W.Random vibration analysis of long-span structures subjected to spatially varying ground motions[J].Soil D ynamics and Earthquake Engineering,2009,29(4):620-629.
[8]张亚辉,智浩,吕峰.结构多点随机地震响应分析及拟静位移计算[J].计算力学学报,2004,21(5):564-570.(Z HAN G Ya-hui,Z HI Hao,LFeng.Seismic random response analysis of multisupported structures and the quasi-static displacement approximation[J].C hinese Journal of C omputational Mechanics,2004,21(5):564-570.(in C hinese))
[9]Alkhaleefi A M,Ali A.An efficient multi-point support-motion random vibration analysis technique[J].Computers&Structures,2002,80(22):1689-1697.
[10]Chen J T,Hong H K,Yeh C S,Chyuan S W.Integral representations and regularizations for a divergent series solution of a beam subjected to support motions[J].Earthquake Engineering and Structural D ynamics,1996,25(9):909-925.
[11]Chen J T,Tsaur D H,Hong H K.An alternative method for transient and random responses of structures subject to support motions[J].Engineering Structures,1997,19(2):162-172.
[12]Lin Y K,Zhang R,Yong Y.Multiply supported pipeline under seismic wave excitations[J].ASCE Journal of Engineering Mechanics,1990,116(5):1094-1108.
[13]Leger P,Ide I M,Paultre P.Multiple-support seismic analysis of large structures[J].Computers&Structures,1990,36(6):1153-1158.
[14]周国良,李小军,刘必灯,齐兴军.大质量法在多点激励分析中的应用,误差分析与改进[J].工程力学,2011,28(1):48-54.(ZHOU Guo-liang,LI Xiao-jun,LIU Bi-deng,QI Xing-jun.Error analysis and improvement of large mass method used in multi-support seismic excitation analysis[J].Engineering Mechanics,2011,28(1):48-54.(in C hinese))
[15]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.(Q U T ie-jun,W AN G Jun-jie,W AN G Q ian-xin.Practical PSD ground motion w ith spatial effect[J].A cta Seismologica Sinica,1996,18(1):55-62.(in C hinese))
[16]冯启民,胡聿贤.空间相关地面运动的数学模型[J].地震工程与工程振动,1981,1(2):1-8.(FENG Qi-min,HU Yu-xian.A mathematical model for spatial seismic ground motion[J].Journal of Earthquake Engineering and Engineering D ynamics,1981,1(2):1-8.(in C hinese))
[17]Loh C H,Yeh Y T.Spatial variation and stochastic modelling of seismic differential ground movement[J].Earthquake Engineering and Structural Dynamics,1988,16(4):583-596.
[18]Der Kiureghian A.A coherency model for spatially varying ground motions[J].Earthquake Engineering and Structural D ynamics,1996,25(1):99-111.
[19]Somerville P G,Mc Laren J P,Sen M K,Helmberger D V.The influence of site conditions on the spatial incoherence of ground motions[J].Structural Safety,1991,10(1):1-13.
[20]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.(LIN Jia-hao,Z HAN G Ya-hui.Pseudo-Excitation Method for R andom V ibration[M].Beijing:Science Press,2004.(in C hinese))
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