大跨复杂结构在多点地震动激励作用下的非线性反应分析
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摘要
地震地面运动是一复杂的时间-空间过程，同一次地震中结构尺度范围内不同点的地震动过程是不同的，这是因为地震波在传播过程中具有行波效应、相干效应和场地效应等。严格来说所有结构的地震反应分析均应考虑地震动空间变异性的影响。但当结构尺度较小或采用整体基础时，这种影响可能较小，常可按一致激励进行分析；随着结构尺度的不断扩大(大跨空间结构)和延长型结构(长大桥梁、管线)的兴建，地震动空间变异性的影响越来越显著。研究表明大跨度结构在抗震设计中应考虑多点激励的影响。另外，就结构本身而言，截面形式多样，尺度相差大，节点形式复杂的复杂结构也将逐步得到应用。本文将围绕这一课题，进行大跨复杂空间结构在多点地震动激励下的非线性反应分析，主要内容包括以下几个方面：
1、非平稳地震动场的人工合成。对大跨空间结构进行多点激励动力分析时，需要一组具有空间相关性的地震波。然而，由于工程场址各不相同，已观测得到的地震动场一般不能符合拟建场地的要求，因此，需要模拟符合特定场地条件和空间相关性要求的非平稳地震动场。本文利用了功率谱、相位谱和幅值谱之间的关系及相位差谱影响地震动非平稳性的特性，用相位差谱的统计模型生成相位谱，用功率谱统计模型和规范反应谱生成幅值谱，用相干函数统计模型考虑相干性，最后人工合成了地震动场，生成的地震动场具有时频非平稳性，适用于规范规定的各类场地类型，可以考虑地震波传播时的行波效应、相干效应和场地效应。
2、结构在多点地震动激励作用下的时程反应分析模型。在分析多点地震动激励下的结构反应时不同文献中曾使用过多种不同的模型，但均未明确讨论过各自的理论基础和应用条件。本文从支座移动时的结构静力平衡方程出发，根据地震动时程输入方式的不同和结构在支座移动随时间变化时的动力平衡方程，总结并推导了多点激励作用下结构地震反应时程分析的四种模型，并以一平面刚架结构为例分析了其理论基础和选择模型的原则。
3、大跨结构在多点地震动激励作用下的反应分析。地震动传播时具有的行波效应、场地效应、不相干效应和衰减效应，都能对结构的反应产生影响，其中衰减效应对相干函数影响很小，可以忽略。本文以四个大跨度结构为例按照不同的工况对地震动传播效应对结构反应的影响进行了研究。研究内容包括单种效应，即行波效应、场地效应、不相干效应对结构反应的影响；两种及三种效应组合，即行波效应和场地效应、行波效应和不相干效应、场地效应和不相干效应、行波效应场地效应和不相干效应对结构反应的影响。
4、国家体育场线性时程反应分析。本文采用基于相位差谱非平稳地震动场的人工合成方法生成了国家体育场的多点地震动激励非平稳地震动场，进行了国家体育场在多点地震动激励作用下的地震反应分析，分别分析结构在X、Y和Z三个方向多点地震动激励和一致地震动激励作用下柱顶、内环梁的最大位移反应和基底反力，将计算结果与一致激励的进行了对比，得出了可供工程设计参考的结论。
5、子结构技术在复杂大跨结构地震反应分析中的应用。为了解决复杂结构自由度数目庞大，计算效率低的问题，本文将近年来发展的子结构技术应用到大跨度复杂结构的非线性分析中。在介绍子结构技术的基本理论、子结构划分和子结构应用的基础上，以一空间两层刚架为例介绍了子结构技术在工程抗震非线性分析中的应用过程并验证了计算结果的精度。
6、国家体育场非线性时程反应分析。在强震作用下，结构会由线性进入非线性。本文将子结构技术应用到国家体育场这一复杂大跨结构的非线性时程分析中，介绍了子结构技术在国家体育场时程分析中的应用，并验证了其动力特性和计算精度，在此基础上对国家体育场结构进行了非线性时程分析，利用人工合成的国家体育场罕遇地震非平稳地震动场，分别研究了国家体育场在一致地震动激励作用下的非线性时程反应和多点地震动激励作用下的非线性时程反应。
The ground motion is a complicated time-space process. There are some characters about the seismic in the process of propagation, such as incoherence effect, wave-passage effect, site-response effect and attenuation affect etc. It has been verified that the ground motions inputting at different supports of large-span structures are different, which may be modeled by phase shifts and coherency losses. The phase shifts are caused by waves propagating, while the coherency losses can be attributed to many factors such as source mechanism, path and local site effects, etc. Significant contributions on these issues have been made, and studies on response of large span structures have shown that the effects of multi-support excitations must be considered. This thesis will work in the nonlinear response analysis of large-span complex structure under specially varying earthquake ground motions, and the main contents are as following.
1. Generation of ground motion field
In the response analysis of large-span structures under specially varying earthquake ground motions, series of seismic waves are needed. Although there have been many recordings about seismic, but the sites about the structures are different, and the present seismic recordings are not satisfying the needing of structures analysis. So, response analysis of structure under seismic need generate artificial ground motions. In this thesis, based on the controlling influence of phase-difference spectrum on the non-stationafity of ground motions, and the relationships of the phase spectrum, power density spectrum and flourier amplitude spectrum, the ground motion field is generated. The statistic model of phase-difference generates the phase-difference spectrum, the statistic model of power spectrum generates the power spectrum, and the statistic model of the coherence function considers the coherence character. The generated ground motion field can consider the influences of incoherency effect, wave-passage effect, and local site effect.
2. Time-history analysis models of structure under multi-support earthquake excitations
There are some models in structure analysis under seismic excitations, and it is very difficult to select a rational model used in the time-history analysis. In this thesis, the analysis models of structure under multi-support seismic excitations are studied. When the earthquake occurred, the ground motion inputs at multiple supports of structures are different. Base on the static equilibrium equation of supports offset, the dynamic equilibrium equation of structure under time-varying base movement is derived, and four different analysis models are presented. A frame structure under seismic excitation is studied using these four models.
3. Response analysis of large-span structures under multi-support excitations
The responses of structure under multi-support excitations are influenced by (1) incoherency effect, (2) wave-passage effect, (3) site-response effect, and (4) attenuation effect. It is found that the influence of attenuation effect is small, and can be ignored. In the thesis, the influences of the three effects to structure response under multi-supports excitations are studied. It is including the influence study of single effect, namely as wave passage effect, spatial incoherent effect and site-response effect, and the influence study of two effects assembly and three effects assembly.
4. Linear response analysis of national stadium under specially varying earthquake ground motions
The time history analysis method is applied to analyze the National Stadium. Spatially varying ground motion time histories are simulated for the analysis. The responses of uniform support excitation and multiple support excitations of the National Stadium are studied, in which the spatially varying excitations and uniform excitation in two horizontal and vertical directions are considered.
5. Application of substructure for large-span complex structure under multi-supports excitations
Substructure method is an advanced analytical technique of FEM, and it is of great value and prospects for engineering. The aims for using substructure is to save computing time and to solve super scale problems under limited computing resource. In this thesis, the using of substructure in large-span complex structure for dynamic nonlinear analysis is studied. The fundamental equation is presented and the application process of substructure method is also discussed, A two-floor spatial frame is studied by the substructure method. It proves that the Substructure method is valid and feasible in dynamic analysis.
6. Nonlinear response analysis of national stadium under specially varying earthquake ground motions
Under the strong earthquake, the structure may be into nonlinear, including geometric nonlinearity and material nonlinearity. The nonlinear responses of uniform support excitation and multiple support excitations of the National Stadium are studied, in which the spatially varying excitations and uniform excitation in two horizontal and vertical directions are also considered.
1、非平稳地震动场的人工合成。对大跨空间结构进行多点激励动力分析时，需要一组具有空间相关性的地震波。然而，由于工程场址各不相同，已观测得到的地震动场一般不能符合拟建场地的要求，因此，需要模拟符合特定场地条件和空间相关性要求的非平稳地震动场。本文利用了功率谱、相位谱和幅值谱之间的关系及相位差谱影响地震动非平稳性的特性，用相位差谱的统计模型生成相位谱，用功率谱统计模型和规范反应谱生成幅值谱，用相干函数统计模型考虑相干性，最后人工合成了地震动场，生成的地震动场具有时频非平稳性，适用于规范规定的各类场地类型，可以考虑地震波传播时的行波效应、相干效应和场地效应。
2、结构在多点地震动激励作用下的时程反应分析模型。在分析多点地震动激励下的结构反应时不同文献中曾使用过多种不同的模型，但均未明确讨论过各自的理论基础和应用条件。本文从支座移动时的结构静力平衡方程出发，根据地震动时程输入方式的不同和结构在支座移动随时间变化时的动力平衡方程，总结并推导了多点激励作用下结构地震反应时程分析的四种模型，并以一平面刚架结构为例分析了其理论基础和选择模型的原则。
3、大跨结构在多点地震动激励作用下的反应分析。地震动传播时具有的行波效应、场地效应、不相干效应和衰减效应，都能对结构的反应产生影响，其中衰减效应对相干函数影响很小，可以忽略。本文以四个大跨度结构为例按照不同的工况对地震动传播效应对结构反应的影响进行了研究。研究内容包括单种效应，即行波效应、场地效应、不相干效应对结构反应的影响；两种及三种效应组合，即行波效应和场地效应、行波效应和不相干效应、场地效应和不相干效应、行波效应场地效应和不相干效应对结构反应的影响。
4、国家体育场线性时程反应分析。本文采用基于相位差谱非平稳地震动场的人工合成方法生成了国家体育场的多点地震动激励非平稳地震动场，进行了国家体育场在多点地震动激励作用下的地震反应分析，分别分析结构在X、Y和Z三个方向多点地震动激励和一致地震动激励作用下柱顶、内环梁的最大位移反应和基底反力，将计算结果与一致激励的进行了对比，得出了可供工程设计参考的结论。
5、子结构技术在复杂大跨结构地震反应分析中的应用。为了解决复杂结构自由度数目庞大，计算效率低的问题，本文将近年来发展的子结构技术应用到大跨度复杂结构的非线性分析中。在介绍子结构技术的基本理论、子结构划分和子结构应用的基础上，以一空间两层刚架为例介绍了子结构技术在工程抗震非线性分析中的应用过程并验证了计算结果的精度。
6、国家体育场非线性时程反应分析。在强震作用下，结构会由线性进入非线性。本文将子结构技术应用到国家体育场这一复杂大跨结构的非线性时程分析中，介绍了子结构技术在国家体育场时程分析中的应用，并验证了其动力特性和计算精度，在此基础上对国家体育场结构进行了非线性时程分析，利用人工合成的国家体育场罕遇地震非平稳地震动场，分别研究了国家体育场在一致地震动激励作用下的非线性时程反应和多点地震动激励作用下的非线性时程反应。
The ground motion is a complicated time-space process. There are some characters about the seismic in the process of propagation, such as incoherence effect, wave-passage effect, site-response effect and attenuation affect etc. It has been verified that the ground motions inputting at different supports of large-span structures are different, which may be modeled by phase shifts and coherency losses. The phase shifts are caused by waves propagating, while the coherency losses can be attributed to many factors such as source mechanism, path and local site effects, etc. Significant contributions on these issues have been made, and studies on response of large span structures have shown that the effects of multi-support excitations must be considered. This thesis will work in the nonlinear response analysis of large-span complex structure under specially varying earthquake ground motions, and the main contents are as following.
1. Generation of ground motion field
In the response analysis of large-span structures under specially varying earthquake ground motions, series of seismic waves are needed. Although there have been many recordings about seismic, but the sites about the structures are different, and the present seismic recordings are not satisfying the needing of structures analysis. So, response analysis of structure under seismic need generate artificial ground motions. In this thesis, based on the controlling influence of phase-difference spectrum on the non-stationafity of ground motions, and the relationships of the phase spectrum, power density spectrum and flourier amplitude spectrum, the ground motion field is generated. The statistic model of phase-difference generates the phase-difference spectrum, the statistic model of power spectrum generates the power spectrum, and the statistic model of the coherence function considers the coherence character. The generated ground motion field can consider the influences of incoherency effect, wave-passage effect, and local site effect.
2. Time-history analysis models of structure under multi-support earthquake excitations
There are some models in structure analysis under seismic excitations, and it is very difficult to select a rational model used in the time-history analysis. In this thesis, the analysis models of structure under multi-support seismic excitations are studied. When the earthquake occurred, the ground motion inputs at multiple supports of structures are different. Base on the static equilibrium equation of supports offset, the dynamic equilibrium equation of structure under time-varying base movement is derived, and four different analysis models are presented. A frame structure under seismic excitation is studied using these four models.
3. Response analysis of large-span structures under multi-support excitations
The responses of structure under multi-support excitations are influenced by (1) incoherency effect, (2) wave-passage effect, (3) site-response effect, and (4) attenuation effect. It is found that the influence of attenuation effect is small, and can be ignored. In the thesis, the influences of the three effects to structure response under multi-supports excitations are studied. It is including the influence study of single effect, namely as wave passage effect, spatial incoherent effect and site-response effect, and the influence study of two effects assembly and three effects assembly.
4. Linear response analysis of national stadium under specially varying earthquake ground motions
The time history analysis method is applied to analyze the National Stadium. Spatially varying ground motion time histories are simulated for the analysis. The responses of uniform support excitation and multiple support excitations of the National Stadium are studied, in which the spatially varying excitations and uniform excitation in two horizontal and vertical directions are considered.
5. Application of substructure for large-span complex structure under multi-supports excitations
Substructure method is an advanced analytical technique of FEM, and it is of great value and prospects for engineering. The aims for using substructure is to save computing time and to solve super scale problems under limited computing resource. In this thesis, the using of substructure in large-span complex structure for dynamic nonlinear analysis is studied. The fundamental equation is presented and the application process of substructure method is also discussed, A two-floor spatial frame is studied by the substructure method. It proves that the Substructure method is valid and feasible in dynamic analysis.
6. Nonlinear response analysis of national stadium under specially varying earthquake ground motions
Under the strong earthquake, the structure may be into nonlinear, including geometric nonlinearity and material nonlinearity. The nonlinear responses of uniform support excitation and multiple support excitations of the National Stadium are studied, in which the spatially varying excitations and uniform excitation in two horizontal and vertical directions are also considered.
引文
[1] A.A. Dumanogluid, K. Soyluk, A stochastic analysis of long span structures subjected to spatially varying ground motions including the site-response effect, Engineering Structures 25 (2003) 1301-1310.
[2] A.S.Nazmy and A.M.Abdel-Ghaffar, Non-linear earthquake response analysis of long-span Cable-stayed Bridge: Application, Earthquake Eng. Struct. Dyn.19,63-76,1990.
[3] A.S.Nazmy and A.M.AbdeI-Ghaffar, Non-linear earthquake response-analysis of long-span Cable-stayed Bridge: Theory, Earthquake Eng. Struct.Dyn.19,45-62,1990.
[4] Abdel-Ghaffar A M, String fellow R G. Response of suspension bridges to traveling earthquake excitation. SDEE, 1984, 3:62-81.
[5] Abrahamson, N.A., Empirical spatial coherency functions for application to soil-structure interaction analyses, Earthquake Spectra, 7:1-28,1991.
[6] B.H.K. Lee, L.Gong And Y.S.WOng, Analysis And Computation Of Nonlinear Dynamic Response Of A Two-Degree-Offreedom System And Its Application In Aeroelasticity, Journal Of Fluids And Structures (1997) 11,225 - 246.
[7] Berrah M K, Eduardo Kausel. A modal combination rule for spatially varying seismic motions. EESD, 1993,22:791-800.
[8] Bonganoff J L, Goldberg J E, Schiff A J. The effect of ground transmission time on the response of long structures. Bull Seism Soc Am, 1965,55:627-640.
[9] Boore, D.M., Phase Derivatives and Simulation of Strong Ground Motions. Bulletin of the Seismological Society of America, 93(3): 1132-1143,2003.
[10]Chin-Hsiung Loh, Bao-Ding Ku, An efficient analysis of structural response for multiple-support seismic excitations, Engng Struct.l995,Volume 17,Number 1:15-26.
[11] Chong, Yun-Loi. Bridge response due to multiple support excitation, 7~(th) Symp.on Earthquake Engineering, Univ.of Rookee, Vol.1,1982.
[12]Clough R. and Penzien J., Dynamics of structures, second edition. McGraw-Hill, Inc,1993.
[13]Conte J.P., Pister K.S. and Mahin, S.A., Nonstationary ARMA modeling of seismic motions, Soil Dynamics and Earthquake Engineering, 11(7): 411-426,1992.
[14]Deodatis, G, Non-stationary stochastic vector processes: seismic ground motion applications. Probabilistic Engng Mech., 11:149-168,1996b.
[15]Deodatis, G, Simulation of ergodic multi-variate stochastic processes. J. Engng Mech., ASCE, 122,1996a.
[16]E.M.Lui, A.Lopes, Dynamic analysis and response of semirigid frames, Engineering Structures, 1997, Vol. 19.No.8:pp644-654.
[17]Ellis GW. and Cakmak A.S., Effect of spatial variability on ARMA modelling of ground motion, Structural Safety, 10(1-3): 181-191,1991.
[18]European Committee for Standardization. Eurocode 8: Structures in seismic regions - design part 2: Bridges. Brussels : European Committee for Standardization, 1995.
[19]F. Behnamfar, Y. Sugimura, Dynamic response of adjacent structures under spatially variable seismic waves, Probabilistic Engineering Mechanics 14 (1999) 33-44.
[20]F.G.A.Al-Bermani and K.Zhu, Noninear elastoplastic analysis of spatial structures under dynamic loading using kinematics Harding models, Engineering Structures, Vol.18, No.8, pp.568-576,1996.
[21]Fleming and E.A.Egeseli, Dynamic behavior of a Cable-stayed Bridge, Earthquake Eng.Struct.Dyn.No8,1-16,1980.
[22]G.C.Lee, Z.Liang, On cross effects of seismic responses of structures, Engineering Structures, 1998,Vol.20, No46, pp.503-509.
[23]G.D.Stefanou, Dynamic response analysis of nonlinear structures using step-by-step integration techniques,Computers&Structures,1995,Vol.57.No.6:pp1063-1070.
[24]Guyan, R. J., "Reduction of Stiffness and Mass Matrices", AIAA Journal, Vol. 3, No. 2 February, 1965.
[25]H.DU,M.K.XIM AND K.M.LIEW, A Nonlinear Finite Element Model For Dynamics of Flexible Manipulators, Mech.Mach.Theory Vol.31,No.8,pp.1109-1119,l 996.
[26]H.Hao,X.N.Duan, Seismic response of asymmetric structures to multiple ground motions, Journal of structural engineering,ASCE,121(11),1995,pp1557-1564.
[27]Hao, H., Oliveira, C. S. and Penzien, J., Multiple-station ground motion processing and simulation based on SMART-1 array data. Nuclear Engng and Design, 111: 293-310.1989.
[28]Harichandran R S , Hawwari A. Response of long-span bridges to spatially varying ground motion. Journal of Structural Engineering, 1996,5:476-483.
[29]Harichandran R.S. and Wang W., Effect of spatially varying seismic excitation on surface lifelines, Proc. Fourth U.S. National Conf. on Earthquake Engineering, 1: 885-94,1990.
[30]Harichandran, R. S. and Vanmarke, E. H., Stochastic Variation of Earthquake Ground Motion in Space and Time, J. of Engineering Mechanics, ASCE, 112(2), 1986.
[31]Harichandran, R. S., Estimation the Spatial Variation of Earthquake Ground Motion from Dense Array Recording, Structural Safety, 10: 219-233,1991.
[32]Harichandran, R. S., Hawwai, A. and Sweidan B. N., Response of Long-span Bridges to Spatially Varying Ground Motion, J. of Structural Engineering, ASCE, 122(5), 1996.
[33]Heredia-Zavoni, E. and Santa-Cruz, S., Conditional Simulation of a class of non-stationary space-time random fields. J. Engng. Mech. 126(4): 398-404,2000.
[34] Hong Hao. Arch response to correlated multiple excitations. EESD, 1993,22: 389-404.
[35]Housner G. W., Characteristics of Strong-motion Earthquakes, BSSA, 37(1),1947.
[36]J.E.Crawford, LJavier M., J.Valancius, D.D.Bogosian and B.W.Dunn, Nonlinear analysis for seismic upgrade studies of existing essential facilities, Computer&Structures, 1997 Vol.64, No.56, pp. 1183-1196.
[37]Jenniggs P. C., Housner G. W. and Tsai N. C, Simulated Earthquake Motions, Tech. Rep. Earthquake Engineering Research Lab., California Inst. of Tech., Pasadena, Calif,1968.
[38] K. Soyluk, A.A. Dumanoglu, Spatial variability effects of ground motions on cable-stayed bridges, Soil Dynamics and Earthquake Engineering 24 (2004) 241-250.
[39]K.J.Bathe,E.Ramm and E.L.Wilson,Finite Element Formulation for Large Deformation Dynamic Analysis.Int.J.Numer.Meth.Engng.,Vol.9,pp.353-386,1975.
[40]K.Nagamani and C.Ganapathy. Finite Element Analysis of Nonlinear Dynamic Response of Articulated Towers, Computers & Structures, Vol.59.No.2,pp.213-223,1996.
[41]Kanda J, Iwasaki R, Ohsaki Y, Masao T, Kitada Y, Sakata K., Generation of simulated earthquake ground motions considering target response spectra of various damping ratios. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K(a): 71-79,1983.
[42]Kaul M. K., Spectrum-consistent time history generation, J. of Engineering Mechanics, ASCE, 104(EM4), 1978.
[43]Kenji Kawano, Katta Venkataramana, Dynamic response and reliability analysis of large offshore structures, Comput. Methods Appl. Mech. Engrg. 168(1999)255-272.
[44]Kiureghian, A. D., A Coherency Model for Spatially Varying Ground Motions, Earthquake Engineering and Structural Dynamics, 25: 99-111,1996.
[45]Kuo Mo Hsiao, Jer Yan Lin,Wen Yi Lin, A consistent Co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams, Comput. Methods Appl. Mech. Engrg. 169 (1999) 1-18.
[46]Lai, S.S.P. Seismic response of a 4-span bridge system subjected to multiple-support ground Excitation, Proc. 4~(th) Canadian Conference Earthquake Engineering, 1983.
[47] Li Y. and Kareem A., Simulation of multivariate nonstationary random processes by FFT. J. Engng Mech., ASME, 117:1037-58,1991.
[48] Loh C.H., Lee S.Z. A seismic displacement analysis of multi-supported bridge to multiple excitations. Soil Dynamics and Earthquake Engineering, 1990, 9(1): 25-33.
[49]M. El-Attar, A. Ghobarah, T.S.Aziz, Non-linear cable response to multiple support periodic excitation, Engineering Structures 22 (2000) 1301-1312.
[50] Mario De Stefano, Giuseppe Faella, An evaluation of the inelastic response of systems under biaxial seismic excitations, Engineering Structures, 1996,Vol.18.No.9:p724-731.
[51]Matsukawa K, Watabe M, Theofanopulos NA, Tohdo M., Phase characteristics of earthquake ground motions and those applications to synthetic ones. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K1: 43-48,1987.
[52] Monti, Giorgio; Nuti, Camillo, Nonlinear response of bridges under multi-support excitation, Proceedings of Engineering Mechanics, Vol2, P1086-1089,1995.
[53]Naraoka K, Watanabe T., Generation of nonstationary earthquake ground motions using phase characteristics. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K1: 37-42,1987.
[54]Nazmy A S , Abdel-Ghaffar A M. Effects of ground motion spatial variability on the response of cable-stayed bridges. EESD, 1992, 21:1—20.
[55]Nazmy Aly S., Abdel-Ghaffar Ahmed M. Non-linear earthquake-response analysis of long-span cable-stayed bridges: theory. Earthquake Engineering and Structural Dynamics, 1990,19(1): 45-62.
[56]Nigam N.C., Phase Properties of a Class of Random Processes, Earthquake Engineering and Structural Dynamics, 10: 711-717,1982.
[57] Ohsaki, Y., On the Significance of Phase Content in Earthquake Ground Motions, Earthquake Engineering and Structural Dynamics, 7: 427-439,1979.
[58]Oliverra Carlos S., Hong Hao, Penzien J., Ground Motion Modeling for Multiple-input Structural Analysis, Structural Safety, 10: 79-93,1991.
[59]R.C.Kar, S.K.Dwivedy, Non-linear dynamics of a slender beam carrying a lumped mass with principal parametric and internal resonance, International Journal of Non-Linear Mechanics 34 (1999)515-529.
[60] Raju Tuladhar and W.H.Dilger, Construction of Geometric Non-linearities to Static and Seismic Response of Cable-Stayed Bridge, 1994 International Symposium on Cable-Stayed B ridges, Shanghai.
[61]Rama Mohan Rao, T.V.S.R. Appa Rao, B. Dattaguru, A new parallel overlapped domain decomposition method for nonlinear dynamic finite element analysis, Computers and Structures 81 (2003)2441 - 2454.
[62]Ramadan O. and Novak M., Simulation of spatially incoherent random ground motions. J. Engng Mech., ASCE, 119: 997-1016,1993.
[63]Rube'n L. Boroschek, Mari'a O. Moroni, Mauricio Sarrazin, Dynamic characteristics of a long span seismic isolated bridge, Engineering Structures 25 (2003) 1479-1490.
[64]S.K. Dwivedy, R.C. Kar, Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions, International Journal of Non-Linear Mechanics 36 (2001) 927-945.
[65]Sang-Hoon Kim, Maria Q. Feng, Fragility analysis of bridges under ground motion with spatial variation, International Journal of Non-Linear Mechanics 38 (2003) 705-721.
[66]Sato T., Muro Y, Wang, H.B., Nishimura, A., Design spectra and phase spectrum modeling to simulate design earthquake motions: a case study through design standerds of railway facilities in Japan. Journal of Natural Disaster Science, 23(2): 89-100,2001.
[67]Sato T., Muro Y., Wang, H.B., Nishimura, A., Phase spectrum modeling to simulate design earthquake motion. Journal of Natural Disaster Science, 24(2): 91-100,2002.
[68]Scanlan R. H. and Sachs K., Earthquake Time Histories and Response Spectra, J. of Engineering Mechanics Division, ASCE, 100(EM4), 1974.
[69]Shinozuka M. and Deodatis G, Simulation of multi-dimensional Gaussian stochastic fields by spectral representation. Appl. Mech. Rev., ASME, 49: 29-53,1996.
[70]Shinozuka M. and Deodatis G, Simulation of stochastic processes by spectral representation. Appl. Mech. Rev., ASME, 44:191-204,1991.
[71]Shinozuka M. and Deodatis G, Stochastic process models for earthquake ground motion. J. Probabilistic Engng Mech., 3:114-123,1988.
[72]Shinozuka M., Stochastic fields and their digital simulation, Stochastic Methods in Structural Dynamics, eds G. I. Schueller and M. Shinozuka, Martinus Nijhoff Publishers, Dordrecht, 93-133,1987.
[73]Shrikhande M. and Gupta V.K., On the characterisation of the phase spectrum for strong motion synthesis. Journal of Earthquake Engineering, 5(4): 465-482,2001.
[74]Shrikhande M. and Gupta V.K., Synthesizing ensembles of spatially correlated accelerograms. J. Engng Mech., ASCE, 124(11): 1185-1192,1998.
[75] Tajimi H., A Statistical Method of Determining the Maximum Response of a Building Structure During an Earthquake, Proc. of 2nd WCEE, 2,1960.
[76] Thrainsson H. and Kiremidjian, A.S., Simulation of digital earthquake accelerograms using the inverse discrete Fourier transform, Earthquake Engng Struct. Dyn, 31:2023-2048,2002.
[77]Vanmarcke, E.H. and Fenton, G.A., Conditioned simulation of local fields of earthquake ground motion. Structural Safety. 10: 247-264,1991.
[78] Vanmarcke, E.H., Fenton, G.A. and Heredia-Zavoni, E., SIMQKE-Ⅱ:Conditioned earthquake ground motion simulator, User's manual, version 2.1. Princeton University,1999.
[79] Vanmarcke, E.H., Heredia-Zavoni, E. and Fenton, G.A.(1993), Conditional simulation of spatially correlated earthquake ground motion. J. Engng Mech., ASCE, 119(11): 2333-2352,1993.
[80] Wilson E.L. Three dimensional static and dynamic analysis of structures: a physical approach with emphasis on earthquake engineering. Computers and Structures, Inc., Berkley, California, 2002.
[81] Y M Xie, An Assessment Of Time Integration Schemes For Non-Linear Dynamic Equations, Journal of Sound and Vibration, (1996)192(1),321-331.
[82] Y.M. Parulekar, K.N. Vaity, G.R. Reddy, K.K. Vaze, H.S. Kushwaha, Earthquake response of inelastic structures, Nuclear Engineering and Design 227 (2004) 185-193.
[83] Y.Zhao, P.R. Wilson,J.D.Stevenson, Nonlinear 3-D Dynamic time history analysis in the reracking modification for a nuclear power plant, Nuclear Engineering and Design, 165(1996) 199-211.
[84] Yamamura N, Hiroshi Tanaka. Response analysis of flexible MDF systems for multiple-support seismic excitations. EESD, 1990,19: 345～357.
[85] Yang Qing-shan and Chen Ying-jun, A practical coherency model for spatial varying ground motions, Structural Engineering and Mechanics, 9(2): 141-152,2000.
[86] Yang Qingshan, Saiidi M.S.,et al. Influence of earthquake ground motion incoherency on multi-support structures. Earthquake Engineering and Engineering Vibration, 2002, 1(2): 167-180.
[87] Yang Qingshan. Practical coherency model for spatially varying ground motions. Structural Engineering and Mechanics, 2000, 9(2): 141-152.
[88] Yutaka Nakamura, Kiureghian A D, David Liu. Multiple-support response spectrum analysis of the golden gate bridge. Berkeley: University of California at Berkeley, 1993.
[89] Zanardo G, Hao H., Modena C. Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion. Earthquake Engineering and Structural Dynamics, 2002, 31(6): 1325-1345.
[90] Zavoni E H, Vanmarcke E H. Seismic random-vibration analysis of multi-support structural systems. J Eng Mechanics, ASCE, 1994,120(5): 1107～1128
[91] 白学丽，叶继红，多维多点输入下大跨度空间网格结构的可靠度分析，第十一界空间结构学术会议论文集，2005．6，460-466。
[92] 陈国兴，孙士军，宰金珉，多维地震动输入下结构地震反应分析，南京建筑工程学院学报，1999年第2期，7-14。
[93] 陈幼平，周宏业，斜拉桥地震破坏的计算研究，地震工程振动，1995，15(3)：127-134
[94] 樊琨，材料非线性结构的动态子结构法，河海大学学报，第27卷第2期，1999年3月，90-95。
[95] 范立础，王君杰，陈玮，非一致地震激励下大跨度斜拉桥的响应特征，计算力学学报，第18卷第3期，2001年8月，358-364。
[96] 范引鹤，弹塑性结构静力分析的子结构方法，东南大学学报，第26卷第4期，73-77，1996．7。
[97] 郭海山，单层球面网壳结构动力稳定性及抗震性能研究，哈尔滨工业大学博士学位论文，2003。
[98] 胡大柱，李宏男，贾连光等，地震作用下输电铁塔非线性动力反应分析，沈阳建筑工程 学院学报(自然科学版)，第20卷第2期，2004年4月，94-96。
[99] 胡世德，范立础，江阴长江公路大桥纵向地震反应分析，同济大学报，1994，22(4)，434-438。
[100] 江建，何放龙，邹银生，高层建筑结构非线性地震反应分析的竖向空间子结构法，四川建筑科学研究，2001年9月第27卷第3期，32-34。
[101] 姜海鹏，杨庆山，一种时频非平稳人造地震动的生成及反应谱拟合方法，工程力学，2000，3(A03)，162-167。
[102] 赖明，地震动的双重过滤白噪声模型，土木工程学报，28(6)，1995。
[103] 李建俊，林家浩，张文首，大跨度结构受多点随机地震激励的响应，计算结构力学及其应用，1995，12(4)，445～452。
[104] 李丽，蒋泽汉，邱新林等，斜拉桥地震响应非线性时程分析，西南交通大学学报，第37卷增刊，P39-44，2002．11。
[105] 李正农，楼梦麟，大跨度桥梁结构地震动输入问题的研究现状，同济大学学报，1999年10月第27卷第5期，592-597。
[106] 梁嘉庆，大跨空间结构在非一致地震输入下的弹性响应分析，东南大学硕士学位论文，2004-3。
[107] 梁嘉庆，叶继红，多点输入下大跨度空间网格结构的地震响应分析，东南大学学报(自然科学版)，2003年9月第33卷第5期，625-630。
[108] 林家浩，张文首，钟万勰，大跨度结构随机地震响应，固体力学学报，第12卷第4期，P319-328，1991．12。
[109] 林家浩，张亚辉，赵岩，大跨度结构抗震分析方法及近期进展，力学进展，第31卷第3期，2001年8月25日，350-360。
[110] 林家浩，钟万勰，张亚辉，大跨度结构抗震计算的随机振动方法，建筑结构学报，2000年2月第21卷第1期，29-36。
[111] 刘枫、肖从真等，首都机场3号航站楼多维多点输入时程地震反应分析，第十一界空间结构学术会议论文集，2005．6，170-176。
[112] 刘洪兵，范立础，大跨桥梁考虑地形及多点激励的地震响应分析，同济大学学报，第31卷第6期，2003年6月，641-646。
[113] 刘洪兵，朱唏，多支承激励地震响应分析的简化反应谱法，中国公路学报，2002．1，15(1)，34-37。
[114] 刘天云，刘光廷，薛颖，地震多点激励结构随机分析方法，世界地震工程，17卷4期，2001年12月，88-92。
[115] 刘先明，大跨度空间网格结构多点输入反应谱理论的研究与应用，东南大学博士学位论文，2003-3。
[116] 刘星庚，伍小平，大跨度桥梁中的几何非线性问题，湖南工程学院学报，第13卷第4期，2003年12月，64-67。
[117] 柳春光，焦双健，城市立交桥结构三维地震反应，地震工程与工程振动，2001，21(2)：41-47。
[118] 楼梦麟编著，结构动力分析的子结构方法，1997。
[119] 马福、李海旺等，大跨度拱桁架在地震作用下的动力稳定性研究，第十一界空间结构学术会议论文集，2005．6，231-235。
[120] 马坤全，大跨度高墩连续梁桥空间地震反应分析，上海铁道学院学报，1995，16(2)： 21-29。
[121] 苗家武，胡世德，范立础，大型桥梁多点激励效应的研究现状与发展，同济大学学报，1999年4月第27卷第2期，189-194。
[122] 牛获涛，基于弹塑性随机动力分析的抗震结构概率设计理论与方法，博士学位论文，哈尔滨建筑大学图书馆，1991。
[123] 潘旦光，楼梦麟，范立础，多点输入下场地非线性地震反应分析计算模型，同济大学学报，2002年12月第30卷第12期，1411-1416。
[124] 彭俊生，张金平，大跨度拱桥几何非线性稳定分析，西南交通大学学报，1993年第3期，105-111。
[125] 蒲军平，计算结构力学中的子结构方法，新疆工学院学报，第15卷第1期，37-42，1994．4。
[126] 秦荣，李秀梅，谢肖礼，大跨度拱几何非线性分析的新方法，工程力学增刊，1999年，47-52。
[127] 邱新林，大跨度斜拉桥非线性地震反应分析，西南交通大学硕士学位论文，2000．1．1。
[128] 邱新林，大跨斜拉桥空间几何非线性动态时程分析，广东公路交通，2003年第1期，24-28。
[129] 屈铁军，王前信，多点输入地震反应分析研究的进展，世界地震工程，1993，9(1)，30-36。
[130] 史志利，李忠献，随机地震动场多点激励下大跨度桥梁地震反应分析方法，地震工程与工程振动，2003年8月第23卷第4期，124-130。
[131] 苏亮、董石麟等，局部场地效应下单层球面网壳的地震反应分析，第十一界空间结构学术会议论文集，2005．6，177-181。
[132] 孙建梅，叶继红等，快速多点输入反应谱法在大跨度空间网格结构中的应用，第十一界空间结构学术会议论文集，2005．6，467-472。
[133] 孙玉萍，空间网架结构弹塑性时程分析的关键技术，甘肃工业大学学报，第24卷第1期，1998年3月，98-103。
[134] 田玉基，杨庆山，地震地面运动作用下结构反应的分析模型，工程力学，2005年22卷第6期，170-174。
[135] 汪梦甫，沈蒲生，建筑结构动力分析的子结构法，湖南大学学报，第21卷，第2期，1994年4月，109-115。
[136] 王成博，史志利，李忠献，随机地震动场多点激励下大跨度连续刚构桥的地震反应分析，地震工程与工程振动，2003年12月第23卷第6期，57-63。
[137] 王航、杨庆山，地震动的空间变异性对多支承结构的影响，世界地震工程，2004，20(1)，54-69。
[138] 王君杰，王前信，大跨度拱桥在空间变化地震动下的响应，振动工学报，1995，8(2)，119-126。
[139] 王理，结构时程分析计算中采用数字地震记录与模拟地震记录的对比分析，建筑结构，第31卷第11期，2001年11月，63-66。
[140] 王前信等，地震多点输入或扰力多点输入时框架结构的反应，地震工程与工程振动，3(2)，1983。
[141] 王前信等，拱式结构对地震多支点输入的反应，地震工程与工程振动，1984，4(2)。
[142] 王文亮，杜作润，结构振动与动态子结构方法，复旦大学出版社，1985。
[143] 王秀丽、丁南生、柴宏，张弦梁结构的抗震特性及参数分析，第十一界空间结构学术会议论文集，2005．6，341-346。
[144] 王永岩编著，动态子结构方法理论及应用，1999。
[145] 夏友柏，王年桥，李爱群，空间刚架受多点随机激励的响应，东南大学学报(自然科学版)，第30卷第4期，2000年7月，48-53。
[146] 向树红，邱吉宝，王大钧，模态分析与动态子结构方法新进展，力学进展，第34卷第3期，289-303，2004．8．25。
[147] 项海帆，斜张桥在行波作用下的地震反应分析，同济大学学报，1983，11(2)：1-9
[148] 徐唱鑫，随机振动，高等教育出版社，1990。
[149] 闫相桥，杜善义，王铎，材料非线性有限元分析中组织结构刚度阵的子结构法，哈尔滨工业大学学报，1989年12月第6期，100-104。
[150] 杨庆山，姜海鹏，基于相位差谱的时—频非平稳人造地震动的反应谱拟合，地震工程与工程振动，2002，22(1)，32-38。
[151] 杨庆山，姜海鹏等，基于相位差谱的时—频非平稳人造地震动的生成，地震工程与工程振动，2001，21(3)，10-16。
[152] 杨庆山，田玉基，工程地震动场模拟，北京：中国建筑工业出版社，2007。
[153] 杨庆山著，现代震害新特点及问题探讨，抗震分析与设计地震动[博士后论文]，北方交通大学，1997．11。
[154] 杨玉民，袁万城，范立础，大跨斜拉桥横向地震反应及其分形特征，同济大学学报，第29卷第1期，2001年1月，16-20。
[155] 杨岳民，刘伯权，杆系结构的动力几何非线性分析，地震工程与工程振动，18卷1期，1998年3月，22-29。
[156] 殷学纲等，结构振动分析的子结构方法，中国铁道出版社，1991。
[157] 虞庐松，大跨度桥梁非线性地震反应研究，西南交通大学博士学位论文，1998-5-1。
[158] 虞庐松，朱唏，大跨度斜拉桥几何非线性地震反应，兰州铁道学院学报，第16卷，第2期，P1-5，1997-6。
[159] 张翠红，大跨度斜拉桥多点激励效应研究，东南大学硕士学位论文，2004-3-1。
[160] 张亚辉，林家浩，香港青马桥抗震分析，应用力学学报，第19卷第3期，2002年9月，25-31。
[161] 赵灿晖，大跨度桥梁地震响应分析中的非—致地震激励模型，西南交通大学学报，第37卷第3期，2002年6月，236-240。
[162] 赵风新，胡聿贤，地震动反应谱与相位差谱的关系，第四届全国地震工程会议论文，大连，1994。
[163] 赵跃宇，大跨径斜拉桥非线性动力学的模型与理论研究，湖南大学博士学位论文，2000．10．1。
[164] 周海亭，陈莲，子结构方法在ANSYS软件中的应用，噪声与振动控制，15-18，第4期，2001．8。
[165] 周建春，寿楠椿，魏琴等，三门峡黄河公路大桥地震反应分析之二，工程力学(增刊)，1993，840-845。
[166] 周建春，魏琴，寿楠椿，群桩—地基土—桥梁结构的相互作用分析，华南理工大学学报(自然科学版)，第30卷第5期，70-74，2002．5。
[167] 邹立华，袁薇，吴慧英，单索面斜拉桥考虑几何非线性地震反应分析，甘肃工业大学学报，第23卷第3期，P83-87，1997．9。
[2] A.S.Nazmy and A.M.Abdel-Ghaffar, Non-linear earthquake response analysis of long-span Cable-stayed Bridge: Application, Earthquake Eng. Struct. Dyn.19,63-76,1990.
[3] A.S.Nazmy and A.M.AbdeI-Ghaffar, Non-linear earthquake response-analysis of long-span Cable-stayed Bridge: Theory, Earthquake Eng. Struct.Dyn.19,45-62,1990.
[4] Abdel-Ghaffar A M, String fellow R G. Response of suspension bridges to traveling earthquake excitation. SDEE, 1984, 3:62-81.
[5] Abrahamson, N.A., Empirical spatial coherency functions for application to soil-structure interaction analyses, Earthquake Spectra, 7:1-28,1991.
[6] B.H.K. Lee, L.Gong And Y.S.WOng, Analysis And Computation Of Nonlinear Dynamic Response Of A Two-Degree-Offreedom System And Its Application In Aeroelasticity, Journal Of Fluids And Structures (1997) 11,225 - 246.
[7] Berrah M K, Eduardo Kausel. A modal combination rule for spatially varying seismic motions. EESD, 1993,22:791-800.
[8] Bonganoff J L, Goldberg J E, Schiff A J. The effect of ground transmission time on the response of long structures. Bull Seism Soc Am, 1965,55:627-640.
[9] Boore, D.M., Phase Derivatives and Simulation of Strong Ground Motions. Bulletin of the Seismological Society of America, 93(3): 1132-1143,2003.
[10]Chin-Hsiung Loh, Bao-Ding Ku, An efficient analysis of structural response for multiple-support seismic excitations, Engng Struct.l995,Volume 17,Number 1:15-26.
[11] Chong, Yun-Loi. Bridge response due to multiple support excitation, 7~(th) Symp.on Earthquake Engineering, Univ.of Rookee, Vol.1,1982.
[12]Clough R. and Penzien J., Dynamics of structures, second edition. McGraw-Hill, Inc,1993.
[13]Conte J.P., Pister K.S. and Mahin, S.A., Nonstationary ARMA modeling of seismic motions, Soil Dynamics and Earthquake Engineering, 11(7): 411-426,1992.
[14]Deodatis, G, Non-stationary stochastic vector processes: seismic ground motion applications. Probabilistic Engng Mech., 11:149-168,1996b.
[15]Deodatis, G, Simulation of ergodic multi-variate stochastic processes. J. Engng Mech., ASCE, 122,1996a.
[16]E.M.Lui, A.Lopes, Dynamic analysis and response of semirigid frames, Engineering Structures, 1997, Vol. 19.No.8:pp644-654.
[17]Ellis GW. and Cakmak A.S., Effect of spatial variability on ARMA modelling of ground motion, Structural Safety, 10(1-3): 181-191,1991.
[18]European Committee for Standardization. Eurocode 8: Structures in seismic regions - design part 2: Bridges. Brussels : European Committee for Standardization, 1995.
[19]F. Behnamfar, Y. Sugimura, Dynamic response of adjacent structures under spatially variable seismic waves, Probabilistic Engineering Mechanics 14 (1999) 33-44.
[20]F.G.A.Al-Bermani and K.Zhu, Noninear elastoplastic analysis of spatial structures under dynamic loading using kinematics Harding models, Engineering Structures, Vol.18, No.8, pp.568-576,1996.
[21]Fleming and E.A.Egeseli, Dynamic behavior of a Cable-stayed Bridge, Earthquake Eng.Struct.Dyn.No8,1-16,1980.
[22]G.C.Lee, Z.Liang, On cross effects of seismic responses of structures, Engineering Structures, 1998,Vol.20, No46, pp.503-509.
[23]G.D.Stefanou, Dynamic response analysis of nonlinear structures using step-by-step integration techniques,Computers&Structures,1995,Vol.57.No.6:pp1063-1070.
[24]Guyan, R. J., "Reduction of Stiffness and Mass Matrices", AIAA Journal, Vol. 3, No. 2 February, 1965.
[25]H.DU,M.K.XIM AND K.M.LIEW, A Nonlinear Finite Element Model For Dynamics of Flexible Manipulators, Mech.Mach.Theory Vol.31,No.8,pp.1109-1119,l 996.
[26]H.Hao,X.N.Duan, Seismic response of asymmetric structures to multiple ground motions, Journal of structural engineering,ASCE,121(11),1995,pp1557-1564.
[27]Hao, H., Oliveira, C. S. and Penzien, J., Multiple-station ground motion processing and simulation based on SMART-1 array data. Nuclear Engng and Design, 111: 293-310.1989.
[28]Harichandran R S , Hawwari A. Response of long-span bridges to spatially varying ground motion. Journal of Structural Engineering, 1996,5:476-483.
[29]Harichandran R.S. and Wang W., Effect of spatially varying seismic excitation on surface lifelines, Proc. Fourth U.S. National Conf. on Earthquake Engineering, 1: 885-94,1990.
[30]Harichandran, R. S. and Vanmarke, E. H., Stochastic Variation of Earthquake Ground Motion in Space and Time, J. of Engineering Mechanics, ASCE, 112(2), 1986.
[31]Harichandran, R. S., Estimation the Spatial Variation of Earthquake Ground Motion from Dense Array Recording, Structural Safety, 10: 219-233,1991.
[32]Harichandran, R. S., Hawwai, A. and Sweidan B. N., Response of Long-span Bridges to Spatially Varying Ground Motion, J. of Structural Engineering, ASCE, 122(5), 1996.
[33]Heredia-Zavoni, E. and Santa-Cruz, S., Conditional Simulation of a class of non-stationary space-time random fields. J. Engng. Mech. 126(4): 398-404,2000.
[34] Hong Hao. Arch response to correlated multiple excitations. EESD, 1993,22: 389-404.
[35]Housner G. W., Characteristics of Strong-motion Earthquakes, BSSA, 37(1),1947.
[36]J.E.Crawford, LJavier M., J.Valancius, D.D.Bogosian and B.W.Dunn, Nonlinear analysis for seismic upgrade studies of existing essential facilities, Computer&Structures, 1997 Vol.64, No.56, pp. 1183-1196.
[37]Jenniggs P. C., Housner G. W. and Tsai N. C, Simulated Earthquake Motions, Tech. Rep. Earthquake Engineering Research Lab., California Inst. of Tech., Pasadena, Calif,1968.
[38] K. Soyluk, A.A. Dumanoglu, Spatial variability effects of ground motions on cable-stayed bridges, Soil Dynamics and Earthquake Engineering 24 (2004) 241-250.
[39]K.J.Bathe,E.Ramm and E.L.Wilson,Finite Element Formulation for Large Deformation Dynamic Analysis.Int.J.Numer.Meth.Engng.,Vol.9,pp.353-386,1975.
[40]K.Nagamani and C.Ganapathy. Finite Element Analysis of Nonlinear Dynamic Response of Articulated Towers, Computers & Structures, Vol.59.No.2,pp.213-223,1996.
[41]Kanda J, Iwasaki R, Ohsaki Y, Masao T, Kitada Y, Sakata K., Generation of simulated earthquake ground motions considering target response spectra of various damping ratios. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K(a): 71-79,1983.
[42]Kaul M. K., Spectrum-consistent time history generation, J. of Engineering Mechanics, ASCE, 104(EM4), 1978.
[43]Kenji Kawano, Katta Venkataramana, Dynamic response and reliability analysis of large offshore structures, Comput. Methods Appl. Mech. Engrg. 168(1999)255-272.
[44]Kiureghian, A. D., A Coherency Model for Spatially Varying Ground Motions, Earthquake Engineering and Structural Dynamics, 25: 99-111,1996.
[45]Kuo Mo Hsiao, Jer Yan Lin,Wen Yi Lin, A consistent Co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams, Comput. Methods Appl. Mech. Engrg. 169 (1999) 1-18.
[46]Lai, S.S.P. Seismic response of a 4-span bridge system subjected to multiple-support ground Excitation, Proc. 4~(th) Canadian Conference Earthquake Engineering, 1983.
[47] Li Y. and Kareem A., Simulation of multivariate nonstationary random processes by FFT. J. Engng Mech., ASME, 117:1037-58,1991.
[48] Loh C.H., Lee S.Z. A seismic displacement analysis of multi-supported bridge to multiple excitations. Soil Dynamics and Earthquake Engineering, 1990, 9(1): 25-33.
[49]M. El-Attar, A. Ghobarah, T.S.Aziz, Non-linear cable response to multiple support periodic excitation, Engineering Structures 22 (2000) 1301-1312.
[50] Mario De Stefano, Giuseppe Faella, An evaluation of the inelastic response of systems under biaxial seismic excitations, Engineering Structures, 1996,Vol.18.No.9:p724-731.
[51]Matsukawa K, Watabe M, Theofanopulos NA, Tohdo M., Phase characteristics of earthquake ground motions and those applications to synthetic ones. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K1: 43-48,1987.
[52] Monti, Giorgio; Nuti, Camillo, Nonlinear response of bridges under multi-support excitation, Proceedings of Engineering Mechanics, Vol2, P1086-1089,1995.
[53]Naraoka K, Watanabe T., Generation of nonstationary earthquake ground motions using phase characteristics. Transactions of the 9th International Conference on Str. Mech. Reactor Tech., K1: 37-42,1987.
[54]Nazmy A S , Abdel-Ghaffar A M. Effects of ground motion spatial variability on the response of cable-stayed bridges. EESD, 1992, 21:1—20.
[55]Nazmy Aly S., Abdel-Ghaffar Ahmed M. Non-linear earthquake-response analysis of long-span cable-stayed bridges: theory. Earthquake Engineering and Structural Dynamics, 1990,19(1): 45-62.
[56]Nigam N.C., Phase Properties of a Class of Random Processes, Earthquake Engineering and Structural Dynamics, 10: 711-717,1982.
[57] Ohsaki, Y., On the Significance of Phase Content in Earthquake Ground Motions, Earthquake Engineering and Structural Dynamics, 7: 427-439,1979.
[58]Oliverra Carlos S., Hong Hao, Penzien J., Ground Motion Modeling for Multiple-input Structural Analysis, Structural Safety, 10: 79-93,1991.
[59]R.C.Kar, S.K.Dwivedy, Non-linear dynamics of a slender beam carrying a lumped mass with principal parametric and internal resonance, International Journal of Non-Linear Mechanics 34 (1999)515-529.
[60] Raju Tuladhar and W.H.Dilger, Construction of Geometric Non-linearities to Static and Seismic Response of Cable-Stayed Bridge, 1994 International Symposium on Cable-Stayed B ridges, Shanghai.
[61]Rama Mohan Rao, T.V.S.R. Appa Rao, B. Dattaguru, A new parallel overlapped domain decomposition method for nonlinear dynamic finite element analysis, Computers and Structures 81 (2003)2441 - 2454.
[62]Ramadan O. and Novak M., Simulation of spatially incoherent random ground motions. J. Engng Mech., ASCE, 119: 997-1016,1993.
[63]Rube'n L. Boroschek, Mari'a O. Moroni, Mauricio Sarrazin, Dynamic characteristics of a long span seismic isolated bridge, Engineering Structures 25 (2003) 1479-1490.
[64]S.K. Dwivedy, R.C. Kar, Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions, International Journal of Non-Linear Mechanics 36 (2001) 927-945.
[65]Sang-Hoon Kim, Maria Q. Feng, Fragility analysis of bridges under ground motion with spatial variation, International Journal of Non-Linear Mechanics 38 (2003) 705-721.
[66]Sato T., Muro Y, Wang, H.B., Nishimura, A., Design spectra and phase spectrum modeling to simulate design earthquake motions: a case study through design standerds of railway facilities in Japan. Journal of Natural Disaster Science, 23(2): 89-100,2001.
[67]Sato T., Muro Y., Wang, H.B., Nishimura, A., Phase spectrum modeling to simulate design earthquake motion. Journal of Natural Disaster Science, 24(2): 91-100,2002.
[68]Scanlan R. H. and Sachs K., Earthquake Time Histories and Response Spectra, J. of Engineering Mechanics Division, ASCE, 100(EM4), 1974.
[69]Shinozuka M. and Deodatis G, Simulation of multi-dimensional Gaussian stochastic fields by spectral representation. Appl. Mech. Rev., ASME, 49: 29-53,1996.
[70]Shinozuka M. and Deodatis G, Simulation of stochastic processes by spectral representation. Appl. Mech. Rev., ASME, 44:191-204,1991.
[71]Shinozuka M. and Deodatis G, Stochastic process models for earthquake ground motion. J. Probabilistic Engng Mech., 3:114-123,1988.
[72]Shinozuka M., Stochastic fields and their digital simulation, Stochastic Methods in Structural Dynamics, eds G. I. Schueller and M. Shinozuka, Martinus Nijhoff Publishers, Dordrecht, 93-133,1987.
[73]Shrikhande M. and Gupta V.K., On the characterisation of the phase spectrum for strong motion synthesis. Journal of Earthquake Engineering, 5(4): 465-482,2001.
[74]Shrikhande M. and Gupta V.K., Synthesizing ensembles of spatially correlated accelerograms. J. Engng Mech., ASCE, 124(11): 1185-1192,1998.
[75] Tajimi H., A Statistical Method of Determining the Maximum Response of a Building Structure During an Earthquake, Proc. of 2nd WCEE, 2,1960.
[76] Thrainsson H. and Kiremidjian, A.S., Simulation of digital earthquake accelerograms using the inverse discrete Fourier transform, Earthquake Engng Struct. Dyn, 31:2023-2048,2002.
[77]Vanmarcke, E.H. and Fenton, G.A., Conditioned simulation of local fields of earthquake ground motion. Structural Safety. 10: 247-264,1991.
[78] Vanmarcke, E.H., Fenton, G.A. and Heredia-Zavoni, E., SIMQKE-Ⅱ:Conditioned earthquake ground motion simulator, User's manual, version 2.1. Princeton University,1999.
[79] Vanmarcke, E.H., Heredia-Zavoni, E. and Fenton, G.A.(1993), Conditional simulation of spatially correlated earthquake ground motion. J. Engng Mech., ASCE, 119(11): 2333-2352,1993.
[80] Wilson E.L. Three dimensional static and dynamic analysis of structures: a physical approach with emphasis on earthquake engineering. Computers and Structures, Inc., Berkley, California, 2002.
[81] Y M Xie, An Assessment Of Time Integration Schemes For Non-Linear Dynamic Equations, Journal of Sound and Vibration, (1996)192(1),321-331.
[82] Y.M. Parulekar, K.N. Vaity, G.R. Reddy, K.K. Vaze, H.S. Kushwaha, Earthquake response of inelastic structures, Nuclear Engineering and Design 227 (2004) 185-193.
[83] Y.Zhao, P.R. Wilson,J.D.Stevenson, Nonlinear 3-D Dynamic time history analysis in the reracking modification for a nuclear power plant, Nuclear Engineering and Design, 165(1996) 199-211.
[84] Yamamura N, Hiroshi Tanaka. Response analysis of flexible MDF systems for multiple-support seismic excitations. EESD, 1990,19: 345～357.
[85] Yang Qing-shan and Chen Ying-jun, A practical coherency model for spatial varying ground motions, Structural Engineering and Mechanics, 9(2): 141-152,2000.
[86] Yang Qingshan, Saiidi M.S.,et al. Influence of earthquake ground motion incoherency on multi-support structures. Earthquake Engineering and Engineering Vibration, 2002, 1(2): 167-180.
[87] Yang Qingshan. Practical coherency model for spatially varying ground motions. Structural Engineering and Mechanics, 2000, 9(2): 141-152.
[88] Yutaka Nakamura, Kiureghian A D, David Liu. Multiple-support response spectrum analysis of the golden gate bridge. Berkeley: University of California at Berkeley, 1993.
[89] Zanardo G, Hao H., Modena C. Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion. Earthquake Engineering and Structural Dynamics, 2002, 31(6): 1325-1345.
[90] Zavoni E H, Vanmarcke E H. Seismic random-vibration analysis of multi-support structural systems. J Eng Mechanics, ASCE, 1994,120(5): 1107～1128
[91] 白学丽，叶继红，多维多点输入下大跨度空间网格结构的可靠度分析，第十一界空间结构学术会议论文集，2005．6，460-466。
[92] 陈国兴，孙士军，宰金珉，多维地震动输入下结构地震反应分析，南京建筑工程学院学报，1999年第2期，7-14。
[93] 陈幼平，周宏业，斜拉桥地震破坏的计算研究，地震工程振动，1995，15(3)：127-134
[94] 樊琨，材料非线性结构的动态子结构法，河海大学学报，第27卷第2期，1999年3月，90-95。
[95] 范立础，王君杰，陈玮，非一致地震激励下大跨度斜拉桥的响应特征，计算力学学报，第18卷第3期，2001年8月，358-364。
[96] 范引鹤，弹塑性结构静力分析的子结构方法，东南大学学报，第26卷第4期，73-77，1996．7。
[97] 郭海山，单层球面网壳结构动力稳定性及抗震性能研究，哈尔滨工业大学博士学位论文，2003。
[98] 胡大柱，李宏男，贾连光等，地震作用下输电铁塔非线性动力反应分析，沈阳建筑工程 学院学报(自然科学版)，第20卷第2期，2004年4月，94-96。
[99] 胡世德，范立础，江阴长江公路大桥纵向地震反应分析，同济大学报，1994，22(4)，434-438。
[100] 江建，何放龙，邹银生，高层建筑结构非线性地震反应分析的竖向空间子结构法，四川建筑科学研究，2001年9月第27卷第3期，32-34。
[101] 姜海鹏，杨庆山，一种时频非平稳人造地震动的生成及反应谱拟合方法，工程力学，2000，3(A03)，162-167。
[102] 赖明，地震动的双重过滤白噪声模型，土木工程学报，28(6)，1995。
[103] 李建俊，林家浩，张文首，大跨度结构受多点随机地震激励的响应，计算结构力学及其应用，1995，12(4)，445～452。
[104] 李丽，蒋泽汉，邱新林等，斜拉桥地震响应非线性时程分析，西南交通大学学报，第37卷增刊，P39-44，2002．11。
[105] 李正农，楼梦麟，大跨度桥梁结构地震动输入问题的研究现状，同济大学学报，1999年10月第27卷第5期，592-597。
[106] 梁嘉庆，大跨空间结构在非一致地震输入下的弹性响应分析，东南大学硕士学位论文，2004-3。
[107] 梁嘉庆，叶继红，多点输入下大跨度空间网格结构的地震响应分析，东南大学学报(自然科学版)，2003年9月第33卷第5期，625-630。
[108] 林家浩，张文首，钟万勰，大跨度结构随机地震响应，固体力学学报，第12卷第4期，P319-328，1991．12。
[109] 林家浩，张亚辉，赵岩，大跨度结构抗震分析方法及近期进展，力学进展，第31卷第3期，2001年8月25日，350-360。
[110] 林家浩，钟万勰，张亚辉，大跨度结构抗震计算的随机振动方法，建筑结构学报，2000年2月第21卷第1期，29-36。
[111] 刘枫、肖从真等，首都机场3号航站楼多维多点输入时程地震反应分析，第十一界空间结构学术会议论文集，2005．6，170-176。
[112] 刘洪兵，范立础，大跨桥梁考虑地形及多点激励的地震响应分析，同济大学学报，第31卷第6期，2003年6月，641-646。
[113] 刘洪兵，朱唏，多支承激励地震响应分析的简化反应谱法，中国公路学报，2002．1，15(1)，34-37。
[114] 刘天云，刘光廷，薛颖，地震多点激励结构随机分析方法，世界地震工程，17卷4期，2001年12月，88-92。
[115] 刘先明，大跨度空间网格结构多点输入反应谱理论的研究与应用，东南大学博士学位论文，2003-3。
[116] 刘星庚，伍小平，大跨度桥梁中的几何非线性问题，湖南工程学院学报，第13卷第4期，2003年12月，64-67。
[117] 柳春光，焦双健，城市立交桥结构三维地震反应，地震工程与工程振动，2001，21(2)：41-47。
[118] 楼梦麟编著，结构动力分析的子结构方法，1997。
[119] 马福、李海旺等，大跨度拱桁架在地震作用下的动力稳定性研究，第十一界空间结构学术会议论文集，2005．6，231-235。
[120] 马坤全，大跨度高墩连续梁桥空间地震反应分析，上海铁道学院学报，1995，16(2)： 21-29。
[121] 苗家武，胡世德，范立础，大型桥梁多点激励效应的研究现状与发展，同济大学学报，1999年4月第27卷第2期，189-194。
[122] 牛获涛，基于弹塑性随机动力分析的抗震结构概率设计理论与方法，博士学位论文，哈尔滨建筑大学图书馆，1991。
[123] 潘旦光，楼梦麟，范立础，多点输入下场地非线性地震反应分析计算模型，同济大学学报，2002年12月第30卷第12期，1411-1416。
[124] 彭俊生，张金平，大跨度拱桥几何非线性稳定分析，西南交通大学学报，1993年第3期，105-111。
[125] 蒲军平，计算结构力学中的子结构方法，新疆工学院学报，第15卷第1期，37-42，1994．4。
[126] 秦荣，李秀梅，谢肖礼，大跨度拱几何非线性分析的新方法，工程力学增刊，1999年，47-52。
[127] 邱新林，大跨度斜拉桥非线性地震反应分析，西南交通大学硕士学位论文，2000．1．1。
[128] 邱新林，大跨斜拉桥空间几何非线性动态时程分析，广东公路交通，2003年第1期，24-28。
[129] 屈铁军，王前信，多点输入地震反应分析研究的进展，世界地震工程，1993，9(1)，30-36。
[130] 史志利，李忠献，随机地震动场多点激励下大跨度桥梁地震反应分析方法，地震工程与工程振动，2003年8月第23卷第4期，124-130。
[131] 苏亮、董石麟等，局部场地效应下单层球面网壳的地震反应分析，第十一界空间结构学术会议论文集，2005．6，177-181。
[132] 孙建梅，叶继红等，快速多点输入反应谱法在大跨度空间网格结构中的应用，第十一界空间结构学术会议论文集，2005．6，467-472。
[133] 孙玉萍，空间网架结构弹塑性时程分析的关键技术，甘肃工业大学学报，第24卷第1期，1998年3月，98-103。
[134] 田玉基，杨庆山，地震地面运动作用下结构反应的分析模型，工程力学，2005年22卷第6期，170-174。
[135] 汪梦甫，沈蒲生，建筑结构动力分析的子结构法，湖南大学学报，第21卷，第2期，1994年4月，109-115。
[136] 王成博，史志利，李忠献，随机地震动场多点激励下大跨度连续刚构桥的地震反应分析，地震工程与工程振动，2003年12月第23卷第6期，57-63。
[137] 王航、杨庆山，地震动的空间变异性对多支承结构的影响，世界地震工程，2004，20(1)，54-69。
[138] 王君杰，王前信，大跨度拱桥在空间变化地震动下的响应，振动工学报，1995，8(2)，119-126。
[139] 王理，结构时程分析计算中采用数字地震记录与模拟地震记录的对比分析，建筑结构，第31卷第11期，2001年11月，63-66。
[140] 王前信等，地震多点输入或扰力多点输入时框架结构的反应，地震工程与工程振动，3(2)，1983。
[141] 王前信等，拱式结构对地震多支点输入的反应，地震工程与工程振动，1984，4(2)。
[142] 王文亮，杜作润，结构振动与动态子结构方法，复旦大学出版社，1985。
[143] 王秀丽、丁南生、柴宏，张弦梁结构的抗震特性及参数分析，第十一界空间结构学术会议论文集，2005．6，341-346。
[144] 王永岩编著，动态子结构方法理论及应用，1999。
[145] 夏友柏，王年桥，李爱群，空间刚架受多点随机激励的响应，东南大学学报(自然科学版)，第30卷第4期，2000年7月，48-53。
[146] 向树红，邱吉宝，王大钧，模态分析与动态子结构方法新进展，力学进展，第34卷第3期，289-303，2004．8．25。
[147] 项海帆，斜张桥在行波作用下的地震反应分析，同济大学学报，1983，11(2)：1-9
[148] 徐唱鑫，随机振动，高等教育出版社，1990。
[149] 闫相桥，杜善义，王铎，材料非线性有限元分析中组织结构刚度阵的子结构法，哈尔滨工业大学学报，1989年12月第6期，100-104。
[150] 杨庆山，姜海鹏，基于相位差谱的时—频非平稳人造地震动的反应谱拟合，地震工程与工程振动，2002，22(1)，32-38。
[151] 杨庆山，姜海鹏等，基于相位差谱的时—频非平稳人造地震动的生成，地震工程与工程振动，2001，21(3)，10-16。
[152] 杨庆山，田玉基，工程地震动场模拟，北京：中国建筑工业出版社，2007。
[153] 杨庆山著，现代震害新特点及问题探讨，抗震分析与设计地震动[博士后论文]，北方交通大学，1997．11。
[154] 杨玉民，袁万城，范立础，大跨斜拉桥横向地震反应及其分形特征，同济大学学报，第29卷第1期，2001年1月，16-20。
[155] 杨岳民，刘伯权，杆系结构的动力几何非线性分析，地震工程与工程振动，18卷1期，1998年3月，22-29。
[156] 殷学纲等，结构振动分析的子结构方法，中国铁道出版社，1991。
[157] 虞庐松，大跨度桥梁非线性地震反应研究，西南交通大学博士学位论文，1998-5-1。
[158] 虞庐松，朱唏，大跨度斜拉桥几何非线性地震反应，兰州铁道学院学报，第16卷，第2期，P1-5，1997-6。
[159] 张翠红，大跨度斜拉桥多点激励效应研究，东南大学硕士学位论文，2004-3-1。
[160] 张亚辉，林家浩，香港青马桥抗震分析，应用力学学报，第19卷第3期，2002年9月，25-31。
[161] 赵灿晖，大跨度桥梁地震响应分析中的非—致地震激励模型，西南交通大学学报，第37卷第3期，2002年6月，236-240。
[162] 赵风新，胡聿贤，地震动反应谱与相位差谱的关系，第四届全国地震工程会议论文，大连，1994。
[163] 赵跃宇，大跨径斜拉桥非线性动力学的模型与理论研究，湖南大学博士学位论文，2000．10．1。
[164] 周海亭，陈莲，子结构方法在ANSYS软件中的应用，噪声与振动控制，15-18，第4期，2001．8。
[165] 周建春，寿楠椿，魏琴等，三门峡黄河公路大桥地震反应分析之二，工程力学(增刊)，1993，840-845。
[166] 周建春，魏琴，寿楠椿，群桩—地基土—桥梁结构的相互作用分析，华南理工大学学报(自然科学版)，第30卷第5期，70-74，2002．5。
[167] 邹立华，袁薇，吴慧英，单索面斜拉桥考虑几何非线性地震反应分析，甘肃工业大学学报，第23卷第3期，P83-87，1997．9。