结构非线性随机地震反应与滤波的理论研究及应用
|
摘要
许多工程结构在强烈随机外激励下都将进入弹塑性变形状态，表现出滞后特性，结构的振动表现为非线性随机振动，因此必须用非线性模型来描述结构，并用非线性随机振动的理论和方法来进行分析。一般来说，结构受到的外激励(地震、风波浪等)属于Markov过程，结构的随机反应也属于Markov过程。在随机振动分析中，这些外激励可当作Gauss过程或滤波Gauss过程，但由于结构的非线性，结构的反应一般并不完全属于Gauss过程。因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。作者主要完成了以下四个方面的工作。
首先，对双线形滞后特性的微分表达式进行了研究，提出了一种新的微分表达式，并给出了证明。本文提出的表达式不仅形式简单，而且便于编程，计算速度快。在此基础上，又提出了双线形滞后体系的随机分段线性化法和双线形滞后体系的随机分段线性滤波器。
其次，通过FPK方程和伊藤随机微分方程，推导和建立了一般非线性工程结构物的单自由度、多自由度随机振动微分方程和随机滤波微分方程。
第三，对非线性结构随机振动近似分析方法中的随机等效线性化法和矩方程法进行了研究。通过已建立的非线性结构物随机振动方程，纳入滞后特性微分表达式，利用随机等效线性化法和矩方程法，计算了工程结构物的随机地震反应。通过大量计算并与Monte Carlo法及其它计算结果比较分析得知，对一般工程结构物，等效线性化法的计算精度能够满足工程应用的要求。
第四，分别按随机等效线性滤波器和作者提出的随机分段线性滤波器，基于受到地震激励的圆钢管混凝土结构物的观测数据，进行了单自由度和多自由度的滤波分析，并与模拟结果进行了对比。研究表明，作者提出的随机分段线性滤波器较等效线性滤波器计算程序简单得多，便于推广应用、而且效率高。这两种滤波器都能很好地去除观测噪声，对实际应用中可能发生的不正确估计观测噪声强度的情况，和不正确估计地震激励强度的情况，两种滤波器都是稳定可靠的。
Under strongly random exterior excitation, most structures will undergo elastic-plastic stage and show hysteretic characteristics, the vibration of structure expresses nonlinear random feature. Therefore nonlinear model must be utilized in order to describe the behavior of this kind of structure, also the theory and methodologies of nonlinear random vibration are necessary for analyzing their response. Generally speaking, exterior excitations that act on structure such as earthquake and wind wavelet, etc. are Markov procedure. The random response of structure as well as exterior excitations is Markov procedure. These exterior excitations can be treated as Gauss procedure or filtering Gauss procedure. But because of the nonlinearity, the response of structure is not absolute Gauss procedure. Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:
Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated. The equations introduced which in simple form can be utilized easily to code a procedure. On this basis, sectionalized linearization of bilinear hysteretic structural characteristics and bilinear hysteretic filtering of structural system are put forward.
Secondly, random vibration and random filtering differential equations of SDOF and MDOF nonlinear structure are established and deduced employing FPK equations and Ito stochastic differential equations.
Thirdly, the methodologies of equivalent linearization and moment equations method in the approximate method for random vibration of nonlinear structure are studied. Random seismic responses of civil engineering structure are
calculated by employing stochastic vibration equations and moment equations methods of nonlinear structures established and stochastic equivalent linearization. In this procedure of calculation, differential expression of hysteretic characteristics and seismic excitation are taken into consideration. Through a great deal of calculation and comparison with the results of Monte Carlo and other methodologies, a conclusion can be drawn that the precision in the calculation of equivalent linearization can satisfy the needs of practical civil applications for general engineering structures.
Lastly, based on the observed data of the concrete-filled tubular structures under seismic excitation, filtering analysis of SDOF and MDOF is done respectively by the methods of stochastic equivalent linearization and sectionalized linearization introduced by the author. The simplicity and efficiency of the proposed methodologies are demonstrated by the comparison. The research indicates that the random sectionalized linearization methodology introduced by the author is more simple and efficient than stochastic equivalent linearization method, so it is convenient for generalizing. The study reveals that all these two filtering can eliminate noise efficiently, they are reliable in the case that the strength of observed noise and seismic excitation estimated incorrectly in practice.
首先，对双线形滞后特性的微分表达式进行了研究，提出了一种新的微分表达式，并给出了证明。本文提出的表达式不仅形式简单，而且便于编程，计算速度快。在此基础上，又提出了双线形滞后体系的随机分段线性化法和双线形滞后体系的随机分段线性滤波器。
其次，通过FPK方程和伊藤随机微分方程，推导和建立了一般非线性工程结构物的单自由度、多自由度随机振动微分方程和随机滤波微分方程。
第三，对非线性结构随机振动近似分析方法中的随机等效线性化法和矩方程法进行了研究。通过已建立的非线性结构物随机振动方程，纳入滞后特性微分表达式，利用随机等效线性化法和矩方程法，计算了工程结构物的随机地震反应。通过大量计算并与Monte Carlo法及其它计算结果比较分析得知，对一般工程结构物，等效线性化法的计算精度能够满足工程应用的要求。
第四，分别按随机等效线性滤波器和作者提出的随机分段线性滤波器，基于受到地震激励的圆钢管混凝土结构物的观测数据，进行了单自由度和多自由度的滤波分析，并与模拟结果进行了对比。研究表明，作者提出的随机分段线性滤波器较等效线性滤波器计算程序简单得多，便于推广应用、而且效率高。这两种滤波器都能很好地去除观测噪声，对实际应用中可能发生的不正确估计观测噪声强度的情况，和不正确估计地震激励强度的情况，两种滤波器都是稳定可靠的。
Under strongly random exterior excitation, most structures will undergo elastic-plastic stage and show hysteretic characteristics, the vibration of structure expresses nonlinear random feature. Therefore nonlinear model must be utilized in order to describe the behavior of this kind of structure, also the theory and methodologies of nonlinear random vibration are necessary for analyzing their response. Generally speaking, exterior excitations that act on structure such as earthquake and wind wavelet, etc. are Markov procedure. The random response of structure as well as exterior excitations is Markov procedure. These exterior excitations can be treated as Gauss procedure or filtering Gauss procedure. But because of the nonlinearity, the response of structure is not absolute Gauss procedure. Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:
Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated. The equations introduced which in simple form can be utilized easily to code a procedure. On this basis, sectionalized linearization of bilinear hysteretic structural characteristics and bilinear hysteretic filtering of structural system are put forward.
Secondly, random vibration and random filtering differential equations of SDOF and MDOF nonlinear structure are established and deduced employing FPK equations and Ito stochastic differential equations.
Thirdly, the methodologies of equivalent linearization and moment equations method in the approximate method for random vibration of nonlinear structure are studied. Random seismic responses of civil engineering structure are
calculated by employing stochastic vibration equations and moment equations methods of nonlinear structures established and stochastic equivalent linearization. In this procedure of calculation, differential expression of hysteretic characteristics and seismic excitation are taken into consideration. Through a great deal of calculation and comparison with the results of Monte Carlo and other methodologies, a conclusion can be drawn that the precision in the calculation of equivalent linearization can satisfy the needs of practical civil applications for general engineering structures.
Lastly, based on the observed data of the concrete-filled tubular structures under seismic excitation, filtering analysis of SDOF and MDOF is done respectively by the methods of stochastic equivalent linearization and sectionalized linearization introduced by the author. The simplicity and efficiency of the proposed methodologies are demonstrated by the comparison. The research indicates that the random sectionalized linearization methodology introduced by the author is more simple and efficient than stochastic equivalent linearization method, so it is convenient for generalizing. The study reveals that all these two filtering can eliminate noise efficiently, they are reliable in the case that the strength of observed noise and seismic excitation estimated incorrectly in practice.
引文
[1] 朱位秋．随机振动．科学出板社，1992
[2] T.K. Caughey. Non-Linear Theory of Random Vibration. Adv. Appl. Mech. 1971, Vol. 11: 209-253
[3] 方同．随机振动理论及其应用．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，123-131
[4] 张相庭．非线性随机振动理论研究进展及在工程上的应用．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，132-139
[5] 朱位秋．非线性随机振动理论的近期进展．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，140-146
[6] 朱位秋．非线性随机振动理论的近期进展．力学进展．1994，24(2)：163-172
[7] 张森文，庄表中等．我国随机振动研究近10年来的进展．振动与冲击．1997，16(3)：1-8
[8] Y.K. Lin. Recent Advances in Stochastic Structural Dynamics. International Conference on Advances in Structural Dynamics, Hong Kong. 2OOO, Vol. 1: 87-78
[9] T.K. Caughey. Derivation and Application of The Fokker-Planck Equation to Discrete Non-Linear Dynamic Systems Subjected to White Random Excitation. The Journal of the Acoustical Society of America. 1963, Vol. 35(11): 1683-1692
[10] Y.K. Wen. Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division, ASCE. 1976,Vol. 102(2): 249-263.
[11] T.K. Caughey. Equivalent LinearizationTechniques. Journal of the Acoustical Society of America. 1963, Vol. 35(11): 1706-1711
[12] W.D. Iwan, I.M. Yang. Application of Statistical Linearization Techniques to Nonlinear Multidegree-of-Freedom System. Journal of Applied Mechanics, Transactions of the ASME. 1972, Vol.
39:545-550
[13] W.D. Iwan. Application of Nonlinear Analysis Techniques. Applied Mechanics in Earthquake Engineering, ASME. 1974, Vol. 8:135-161
[14] T. S. Atalik, S. Utku. Linearization of Multi-degree of Freedom Non-Linear Systems. Earthquack Engineering and Structural Dynamics. 1976, Vol. 4(4): 411-420
[15] I. Elishakoff, X.T. Zhang. An Appraisal of Different Stochastic Linearization Techniques. Journal of Sound and Vibration. 1992, Vo1.153.370-375
[16] 张相庭．等平方能量法计算非线性结构随机振动．振动与冲击．1992， 11：38-42
[17] 张相庭．加权能量法计算非线性随机振动的研究．非线性振动、分又 及浑沌．天大出版社．1992，139-144
[18] 王国砚，张相庭．非线性随机振动中基于能量c次方的等效线性化方法．振动与冲击．1998，9：6-9
[19] 王国砚．非线性随机振动中的等效线性化方法研究及在工程中的应用．同济大学博士学位论文．1999
[20] R. 7. Cheng, G.E. Young. Method and Gaussian Criterion for Statistical Linearization of Stochastic Parameterically and Externally Excited Nonlinear Systems. J. Appl. Mech. ASME. 1989, Vol. 56(1):179-185
[21] L.D. Lutes. Approximate Technique for Treating Random Vibration of Hysteretic System. J. Acoust. Soc. Am. 1970, Vol. 48:299-306
[22] T.K. Caughey. On the Response of Nonlinear Oscillators to Stochastic Excitation. Prob. Engrg.Mech. 1986, Vol. 1(1):2-4
[23] 朱位秋，余金寿．预测非线性系统响应的等效非线性系统法．固体力学学报．1989，Vol．10(1)：34-44
[24] W.Q. Zhu, J.S. Yu. The Equivalent Nonlinear System Method. J. Sound. Vib. 1989,129:385-395
[25] G.Q. Cai, Y.K. Lin. A New Approximate Solution Technique for Randomly Excited Nonlinear Oscillators. Int. J. Non-Lin. Mech. 1988,23:409-420
[26] 佘锟，沈德安．滞回系统随机振动的累积量截断法．振动与冲击．1989，
2：1-11
[27] 刘强，丁文镜．非线性系统随机振动的非高斯矩法．力学学报．1986，18：439-447
[28] 戴德成，蔡晶．非线性随机振动的一种改进的非高斯矩法．振动工程学报．1989，2：70-74
[29] 朱位秋．能量平均法及其应用．力学进展．1987，17：342-351
[30] 鲁民清．非线性随机振动中的广义胞映射法．固体力学学报．1993，14(4)：368-371
[31] M. Shinozhk.Simulation of Multivariate and Multidimensional Random Processes. The Journal of the Acoustical Society of America. 1972, Vol. 49(1):357-368
[32] M. Shinozhk, C.M. Jan. Digital Simulation of Random Processes and its Applications. Journal of Sound and Vibration. 1972, Vol. 25(1): 111-128
[33] M. Shinozhk, YoK. Wen. Monte-Carlo Solution of Nonlinear Vibrations. AIAA Journal. 1972, Vol. 10(1):37-40
[34] 星谷胜．随机振动分析．常宝琦译．地震出版社，1977
[35] 沈聚敏，周锡元，高小旺，刘晶波．抗震工程学．中国建筑工业出版社，2000
[36] 高钟毓．工程系统中的随机过程-随机系统分析与最优滤波．清华大学出版社，1989
[37] R.E. Kalman. A New Approach to Linear Filtering and Prediction Problems. J. Basic Eng. 1960, 82: 35-45,
[38] R.E. Kalman, R.S. Bucy. New Results in Linear Filtering and Prediction Theory. J. Basic Eng. 1961,83:95-108
[39] RoL. Stratonovich. Conditional Markov Processes and Their Application to the Theory of Optimal Control. American Elsevier, 1968
[40] H. J. Kushner. Dynamic Equations for Optimal Nonlinear Filtering. Journal of Differential Equations. 1967,3:179-190
[41] R.Minai,Y.Suzuki. Stochastic Estimates of Nonlinear Dynamic Systems. Stochastic Approaches in Earthquake Engineering, U.S.-Japan Joint Seminar, Boca Raton, Florida, USA.
Springer-Verlag, 1987:204-230
[42] 砂原善文．非线形滤波理论展望．计测制御．1976，Vol．15(12)：923-934
[43] G.W. Housner. et. Structural Control:Past, Present, and Future. Journal of Engineering Mechanics. 1997, Vol. 123(9):897-971
[44] 阎维明，周福霖，谭平．土木工程结构振动控制的研究进展．世界地震工程．1997，13(2)：8-20
[45] 张俊平，李新平，周福霖．桥梁结构振动控制发展及存在的问题．世界地震工程．1997，14(2)：9-16
[46] 刘季．结构抗震抗风振动控制．工程力学(增刊)．1997，24-28
[47] 复旦大学．概率论(第三册)-随机过程．人们教育出版社，1981
[48] 欧进萍，王光远．结构随机振动．高等教育出版社，1998
[49] 武宝亭等．随机过程与随机微分方程．电子科技大学出版社，1993
[50] 日本道路协会．道路示方书·同解说-V耐震设计篇．丸善株式会社，1992
[51] 韩林海．钢管混凝土结构．科学出版社，2000
[52] 韩林海，陶忠，阎维波．圆钢管混凝土构件弯矩-曲率滞回性能研究．地震工程与工程振动．2000(3)：50-59
[53] 韩林海，陶忠．圆钢管混凝土压弯构件荷载-位移滞回性能分析．地震工程与工程振动．2001，21(1)：64-73
[54] 陶忠，韩林海．方钢管混凝土压弯构件滞回性能的试验研究．地震工程与工程振动．2001，21(1)：74-78
[55] M.K. Kaul, J. Penzien. Stochastic Seismic Analysis of Yielding Offshore Towers. Journal of the Engineering Mechanics Division, ASCE. 1974, Vol. 100(5):1025-1038
[56] T. Kobori, R. Minai, Y. Suzuki. Stochastic Seismic Response of Hysteretic Structures. Bulletin of the Disaster Prevention Research Institute, Kyoto University. 1976, Vol. 26:57-70
[57] Y. Suzuki, R. Minai. Application of Stochastic differential equations to seismic reliability analysis of hysteretic structures. Probabilistic Engineering Mechanics. 1988, Vol. 3(1):43-52
[58] 周纪卿．非线性振动．西安交通大学出版社，1998
[59] 杨有福，韩林海，范喜哲．钢管混凝土动力性能研究现状．哈尔滨建筑大学学报．2000，33(5)：40-46
[60] 严国敏．钢管混凝土组合桥墩高架桥的设计与实施-日本新干线高架桥的快速施工(之四)．国外桥梁．1999，1：42-44
[61] Y. Suzuki. Seismic Reliability Analysis of Hysteretic Structures Based on Stochastic Differential Equations. Ph.D. Thesis, Kyoto University, Japan. 1985.
[62] M. Shinozuka, Y. Sato. Simulation of Nonstationary Random Processes. Journal of the Engineering Mechanics Division. ASCE.1967,93:11-40
[63] A.H. Jazwinski. Stochsctic Processes and Filtering Theory. Academic Press, New York. 1970
[64] B．D．G安德森，J．B．摩尔．最佳滤波．卢伯英译．国防工业出版社，1983
[65] R. Minai, Y. Suzuki. Stochastic Estimates of Nonlinear Dynamic Systems. Lecture Notes in Engineering. Edited by Y.K. lin and R. minai, Springer-Verlag, New york. 1987, Vol. 32:204-230
[66] 南井良一郎．建筑构造物确率论的地震応答解析．京都大学防災研究所年报．1981，4：第24号A
[67] 田琪，铃木祥之，南井良一郎．地震応答观测基履歴构造物非正规确率推定．日本建筑学会1990年度大会学术讲演梗概集，日本．1990：587-588
[68] 胡聿贤．地震工程学．地震出版社，1988
[69] 范立础．桥梁抗震．同济大学出版社，1997
[70] 庄表中等．非线性随机振动理论及应用．浙江大学出版社，1986
[71] 陈英俊，甘幼琛，于希哲．结构随机振动．人们交通出版社，1993
[72] 克拉夫，彭津．结构动力学．王光远等译．科学出版社，1981
[73] 陈宝春．钢管混凝土拱桥设计与施工．人们交通出版社，1999
[74] 钟万勰，林家浩．大跨度桥梁分析方法的一些进展．大连理工大学学报．2000，40(2)：127-135
[75] 林家浩．随机地震相应的确定性算法．地震工程与工程振动．1985，Vol．5(1)：89-94
[76] 胡聿贤，周锡元．地震工程的跨世纪发展趋势．工程抗震．1999，1：3-9
[77] 王东升，郭恩栋．钢筋混凝土圆形截面柱式桥墩抗震性能评价．世界地震工程．2001，17(1)：98-102
[78] 赵雷，陈虬，路湛沁．钢筋混凝土结构非线性随机地震响应分析．工程力学．1999，Vol．16(5)：21-32
[79] 王军，林家浩．剪切型非线性滞迟系统随机地震响应的虚拟激励分析．固体力学学报．2001，22(1)：23-30
[80] 朱晞．用抗震设计反应谱计算梁式桥桥墩的简化公式．土木工程学报．1985，18(3)：44-52
[81] 朱晞，王大庆．用抗震设计反应谱计算桩基桥墩的简化公式．土木工程学报．1992，25(6)：51-57
[82] 陈兴冲．桥墩自振频率的能量公式．土木工程学报．1999，32(5)：76-80
[83] 范立础，王君杰．桥梁抗震设计规范的现状与发展趋势．地震工程与工程振动．2001，21(2)：70-77
[84] 范立础，王志强．我国桥梁隔震技术的应用．振动工程学报．1999，12(2)：173-181
[85] 周云，周福霖．桥梁震害与减震防灾新对策．世界地震工程．1997，13(1)：8-15
[86] 杨海荣，郑琦．日本公路桥的抗震鉴定和加固．国外桥梁．1997，2：69-77．82
[87] 欧进萍，吴波．弹塑性随机振动系统中恢复力学数学模型的若干形式．应用力学学报．1995，12(1)：63-70
[88] 杜修为．钢筋混凝土房屋结构弹塑性地震反应分析文献综述．世界地震工程．1990，4：1-7
[89] 薛伟辰，张志铁．钢筋混凝土结构非线性全过程分析方法及其应用．计算力学学报．1999，16(3)：334-342
[90] 刘南科，周基岳．钢筋混凝土框架的非线性全过程分析．土木工程学报．1990，23(4)：2-14
[91] 薛伟辰，吕志涛．混凝土杆系结构滞回全过程分析．工程力学．1996，13(3)：8-16
[92] 杜修力．结构弹塑性地震反应现状评述．工程力学．1994，11(2)：99-104
[93] 刘勇生．桥梁结构抗震研究的文献综述．世界地震工程．1992，1：48-55，62
[94] 王君杰．一般阻尼线性系统随机地震反应分析．工程力学．1994，11(4)：
109-114
[95] 田千里，关国雄，张佑启．具有滞迟耗能装置的高层建筑结构的随机响应分析．地震工程与工程振动．1995，15(2)：109-117
[96] 钱培风．高层建筑的抗震问题．世界地震工程．1992，3：15-21
[97] 刘庆华，徐虎．单柱式钢筋混凝土桥墩在水平地震作用下的损伤分析．工程力学．1997，3：108-112
[98] 胡世德，叶爱君．独柱式多层立交桥非线性地震反应分析．土木工程学报．1997，30(4)：19-25
[99] 周锡元，李中锡．规则型隔震桥梁结构的简化分析方法．土木工程学报．2001，34(3)：53-58，66
[100] 田琪，陈兴冲．拼装式桥墩接头的承载能力与滞回特性的试验研究．工程力学．1999，16(2)：107-113
[101] 章建军，刘进．兵库县南部地震中钢管桥墩损坏的数值模拟．国外桥梁．2000，2：59-64
[102] 严国敏．采用钢管加劲的混凝土组合结构高桥墩(之五)．国外桥梁．1999，1：45-47
[103] 李惠，王震宇．钢管高强混凝土叠合柱弯矩-曲率关系的合成模型．计算力学学报．2000，17(2)：184-191
[104] Y.Suzuki, R. Minai. A Method of Seismic Response Analysis of Hysteretic Structures Based on Stochastic Differential Equations. Proceedings of the Eighth World Conference on Earthquake Engnineering, San Francisco. 1984:459-466
[105] 赵雷．随机参数结构动力分析方法及地震可靠度研究．西南交通大学博士学位论文．1996
[106] 赵灿晖．大跨度钢管混凝土拱桥的地震响应研究．西南交通大学博士学位论文．2001
[107] 朱东生．桥梁抗震设计中几个问题的研究．西南交通大学博士学位论文．1999
[108] 陈兴冲．重力式桥墩-地基的线性及非线性动力性态研究．北方交通大学博士学位论文．1996
[109] 李乔．薄壁曲箱梁的空间分析理论．西南交通大学博士学位论文．1988
[110] K.J. Mθrk. Stochastic Response and Reliability Analysis of Hysteretic Structures. Ph.D. Thesis, university of ialborg,
Danmark. 1989
[111] G.Q. Cai, Y.K. Lin. Random Vibration of Strongly Nonlinear System. Journal of Nonlinear Dynamics. 2001, Vol. 24:3-15
[112] S. Erdal. Analysis of Earthquake Record from Structures:an Overview. NATO Advanced Research Workshop on Strong Motion Instrumentation for CivilEngineering Structures, Istanbul, Turkey. 1999:91-107
[113] S.F. Wojtkiewicz, L.A. Bergman, G. Turan. Covariance Control of a Hysteretic System. The 2nd World Conference on Structural Control, Kyoto, Japan. 1998:1967-1974
[114] Z.G. Ying, W.Q. Zhu, Y.Q. Ni, J.M. Ko. Stochastic Averaging of Duhem Hysteretic System. Journal of Sound and Vibration. 2OO2, Vol. 254:91-104
[115] M. Vasta, G.I. Schueller. Phase Space Reduction in Stochastic Dynamics. Journal of Engineering Mechanics. 2000, Vol. 126(6): 626-632
[116] Y.K. Lin, G.Q. Cai. Some Thoughts on Averaging Techniques in Stochastic Dynamics. Probabilistic Engineering Mechanic. 2000, Vol.15(1):7-14
[117] W.Q. Zhu, Z.G. Ying, Y. Suzuki. Optimal Nonlinear Feedback Control of Building Structures with AMD under Non-White Random Ground Acceleration Excitation. Internation Conference on Advances in Structural Dynamics. Hong Kong, China. 2000:13-15
[118] A. Elremaily. Seismic Behavior of High Strength Concrete Filled Tube(CFT)Columns. First International Conference on High Strength Concrete. Kona, Hawaii. 1997:13-18
[119] M. Shinozuka. Recent Developments in Stochastic Mechanics Relevant to Earthquake Engineering. Journal of Engineering Mechanics. 1996
[120] 铁道総合技术研究所．铁道构造物等设计标准·同解说-耐震设计．丸善株式会社．日本，东京．2000
[2] T.K. Caughey. Non-Linear Theory of Random Vibration. Adv. Appl. Mech. 1971, Vol. 11: 209-253
[3] 方同．随机振动理论及其应用．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，123-131
[4] 张相庭．非线性随机振动理论研究进展及在工程上的应用．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，132-139
[5] 朱位秋．非线性随机振动理论的近期进展．一般力学(动力学、振动与控振)最新进展．科学出板社，1994，140-146
[6] 朱位秋．非线性随机振动理论的近期进展．力学进展．1994，24(2)：163-172
[7] 张森文，庄表中等．我国随机振动研究近10年来的进展．振动与冲击．1997，16(3)：1-8
[8] Y.K. Lin. Recent Advances in Stochastic Structural Dynamics. International Conference on Advances in Structural Dynamics, Hong Kong. 2OOO, Vol. 1: 87-78
[9] T.K. Caughey. Derivation and Application of The Fokker-Planck Equation to Discrete Non-Linear Dynamic Systems Subjected to White Random Excitation. The Journal of the Acoustical Society of America. 1963, Vol. 35(11): 1683-1692
[10] Y.K. Wen. Method for Random Vibration of Hysteretic Systems. Journal of the Engineering Mechanics Division, ASCE. 1976,Vol. 102(2): 249-263.
[11] T.K. Caughey. Equivalent LinearizationTechniques. Journal of the Acoustical Society of America. 1963, Vol. 35(11): 1706-1711
[12] W.D. Iwan, I.M. Yang. Application of Statistical Linearization Techniques to Nonlinear Multidegree-of-Freedom System. Journal of Applied Mechanics, Transactions of the ASME. 1972, Vol.
39:545-550
[13] W.D. Iwan. Application of Nonlinear Analysis Techniques. Applied Mechanics in Earthquake Engineering, ASME. 1974, Vol. 8:135-161
[14] T. S. Atalik, S. Utku. Linearization of Multi-degree of Freedom Non-Linear Systems. Earthquack Engineering and Structural Dynamics. 1976, Vol. 4(4): 411-420
[15] I. Elishakoff, X.T. Zhang. An Appraisal of Different Stochastic Linearization Techniques. Journal of Sound and Vibration. 1992, Vo1.153.370-375
[16] 张相庭．等平方能量法计算非线性结构随机振动．振动与冲击．1992， 11：38-42
[17] 张相庭．加权能量法计算非线性随机振动的研究．非线性振动、分又 及浑沌．天大出版社．1992，139-144
[18] 王国砚，张相庭．非线性随机振动中基于能量c次方的等效线性化方法．振动与冲击．1998，9：6-9
[19] 王国砚．非线性随机振动中的等效线性化方法研究及在工程中的应用．同济大学博士学位论文．1999
[20] R. 7. Cheng, G.E. Young. Method and Gaussian Criterion for Statistical Linearization of Stochastic Parameterically and Externally Excited Nonlinear Systems. J. Appl. Mech. ASME. 1989, Vol. 56(1):179-185
[21] L.D. Lutes. Approximate Technique for Treating Random Vibration of Hysteretic System. J. Acoust. Soc. Am. 1970, Vol. 48:299-306
[22] T.K. Caughey. On the Response of Nonlinear Oscillators to Stochastic Excitation. Prob. Engrg.Mech. 1986, Vol. 1(1):2-4
[23] 朱位秋，余金寿．预测非线性系统响应的等效非线性系统法．固体力学学报．1989，Vol．10(1)：34-44
[24] W.Q. Zhu, J.S. Yu. The Equivalent Nonlinear System Method. J. Sound. Vib. 1989,129:385-395
[25] G.Q. Cai, Y.K. Lin. A New Approximate Solution Technique for Randomly Excited Nonlinear Oscillators. Int. J. Non-Lin. Mech. 1988,23:409-420
[26] 佘锟，沈德安．滞回系统随机振动的累积量截断法．振动与冲击．1989，
2：1-11
[27] 刘强，丁文镜．非线性系统随机振动的非高斯矩法．力学学报．1986，18：439-447
[28] 戴德成，蔡晶．非线性随机振动的一种改进的非高斯矩法．振动工程学报．1989，2：70-74
[29] 朱位秋．能量平均法及其应用．力学进展．1987，17：342-351
[30] 鲁民清．非线性随机振动中的广义胞映射法．固体力学学报．1993，14(4)：368-371
[31] M. Shinozhk.Simulation of Multivariate and Multidimensional Random Processes. The Journal of the Acoustical Society of America. 1972, Vol. 49(1):357-368
[32] M. Shinozhk, C.M. Jan. Digital Simulation of Random Processes and its Applications. Journal of Sound and Vibration. 1972, Vol. 25(1): 111-128
[33] M. Shinozhk, YoK. Wen. Monte-Carlo Solution of Nonlinear Vibrations. AIAA Journal. 1972, Vol. 10(1):37-40
[34] 星谷胜．随机振动分析．常宝琦译．地震出版社，1977
[35] 沈聚敏，周锡元，高小旺，刘晶波．抗震工程学．中国建筑工业出版社，2000
[36] 高钟毓．工程系统中的随机过程-随机系统分析与最优滤波．清华大学出版社，1989
[37] R.E. Kalman. A New Approach to Linear Filtering and Prediction Problems. J. Basic Eng. 1960, 82: 35-45,
[38] R.E. Kalman, R.S. Bucy. New Results in Linear Filtering and Prediction Theory. J. Basic Eng. 1961,83:95-108
[39] RoL. Stratonovich. Conditional Markov Processes and Their Application to the Theory of Optimal Control. American Elsevier, 1968
[40] H. J. Kushner. Dynamic Equations for Optimal Nonlinear Filtering. Journal of Differential Equations. 1967,3:179-190
[41] R.Minai,Y.Suzuki. Stochastic Estimates of Nonlinear Dynamic Systems. Stochastic Approaches in Earthquake Engineering, U.S.-Japan Joint Seminar, Boca Raton, Florida, USA.
Springer-Verlag, 1987:204-230
[42] 砂原善文．非线形滤波理论展望．计测制御．1976，Vol．15(12)：923-934
[43] G.W. Housner. et. Structural Control:Past, Present, and Future. Journal of Engineering Mechanics. 1997, Vol. 123(9):897-971
[44] 阎维明，周福霖，谭平．土木工程结构振动控制的研究进展．世界地震工程．1997，13(2)：8-20
[45] 张俊平，李新平，周福霖．桥梁结构振动控制发展及存在的问题．世界地震工程．1997，14(2)：9-16
[46] 刘季．结构抗震抗风振动控制．工程力学(增刊)．1997，24-28
[47] 复旦大学．概率论(第三册)-随机过程．人们教育出版社，1981
[48] 欧进萍，王光远．结构随机振动．高等教育出版社，1998
[49] 武宝亭等．随机过程与随机微分方程．电子科技大学出版社，1993
[50] 日本道路协会．道路示方书·同解说-V耐震设计篇．丸善株式会社，1992
[51] 韩林海．钢管混凝土结构．科学出版社，2000
[52] 韩林海，陶忠，阎维波．圆钢管混凝土构件弯矩-曲率滞回性能研究．地震工程与工程振动．2000(3)：50-59
[53] 韩林海，陶忠．圆钢管混凝土压弯构件荷载-位移滞回性能分析．地震工程与工程振动．2001，21(1)：64-73
[54] 陶忠，韩林海．方钢管混凝土压弯构件滞回性能的试验研究．地震工程与工程振动．2001，21(1)：74-78
[55] M.K. Kaul, J. Penzien. Stochastic Seismic Analysis of Yielding Offshore Towers. Journal of the Engineering Mechanics Division, ASCE. 1974, Vol. 100(5):1025-1038
[56] T. Kobori, R. Minai, Y. Suzuki. Stochastic Seismic Response of Hysteretic Structures. Bulletin of the Disaster Prevention Research Institute, Kyoto University. 1976, Vol. 26:57-70
[57] Y. Suzuki, R. Minai. Application of Stochastic differential equations to seismic reliability analysis of hysteretic structures. Probabilistic Engineering Mechanics. 1988, Vol. 3(1):43-52
[58] 周纪卿．非线性振动．西安交通大学出版社，1998
[59] 杨有福，韩林海，范喜哲．钢管混凝土动力性能研究现状．哈尔滨建筑大学学报．2000，33(5)：40-46
[60] 严国敏．钢管混凝土组合桥墩高架桥的设计与实施-日本新干线高架桥的快速施工(之四)．国外桥梁．1999，1：42-44
[61] Y. Suzuki. Seismic Reliability Analysis of Hysteretic Structures Based on Stochastic Differential Equations. Ph.D. Thesis, Kyoto University, Japan. 1985.
[62] M. Shinozuka, Y. Sato. Simulation of Nonstationary Random Processes. Journal of the Engineering Mechanics Division. ASCE.1967,93:11-40
[63] A.H. Jazwinski. Stochsctic Processes and Filtering Theory. Academic Press, New York. 1970
[64] B．D．G安德森，J．B．摩尔．最佳滤波．卢伯英译．国防工业出版社，1983
[65] R. Minai, Y. Suzuki. Stochastic Estimates of Nonlinear Dynamic Systems. Lecture Notes in Engineering. Edited by Y.K. lin and R. minai, Springer-Verlag, New york. 1987, Vol. 32:204-230
[66] 南井良一郎．建筑构造物确率论的地震応答解析．京都大学防災研究所年报．1981，4：第24号A
[67] 田琪，铃木祥之，南井良一郎．地震応答观测基履歴构造物非正规确率推定．日本建筑学会1990年度大会学术讲演梗概集，日本．1990：587-588
[68] 胡聿贤．地震工程学．地震出版社，1988
[69] 范立础．桥梁抗震．同济大学出版社，1997
[70] 庄表中等．非线性随机振动理论及应用．浙江大学出版社，1986
[71] 陈英俊，甘幼琛，于希哲．结构随机振动．人们交通出版社，1993
[72] 克拉夫，彭津．结构动力学．王光远等译．科学出版社，1981
[73] 陈宝春．钢管混凝土拱桥设计与施工．人们交通出版社，1999
[74] 钟万勰，林家浩．大跨度桥梁分析方法的一些进展．大连理工大学学报．2000，40(2)：127-135
[75] 林家浩．随机地震相应的确定性算法．地震工程与工程振动．1985，Vol．5(1)：89-94
[76] 胡聿贤，周锡元．地震工程的跨世纪发展趋势．工程抗震．1999，1：3-9
[77] 王东升，郭恩栋．钢筋混凝土圆形截面柱式桥墩抗震性能评价．世界地震工程．2001，17(1)：98-102
[78] 赵雷，陈虬，路湛沁．钢筋混凝土结构非线性随机地震响应分析．工程力学．1999，Vol．16(5)：21-32
[79] 王军，林家浩．剪切型非线性滞迟系统随机地震响应的虚拟激励分析．固体力学学报．2001，22(1)：23-30
[80] 朱晞．用抗震设计反应谱计算梁式桥桥墩的简化公式．土木工程学报．1985，18(3)：44-52
[81] 朱晞，王大庆．用抗震设计反应谱计算桩基桥墩的简化公式．土木工程学报．1992，25(6)：51-57
[82] 陈兴冲．桥墩自振频率的能量公式．土木工程学报．1999，32(5)：76-80
[83] 范立础，王君杰．桥梁抗震设计规范的现状与发展趋势．地震工程与工程振动．2001，21(2)：70-77
[84] 范立础，王志强．我国桥梁隔震技术的应用．振动工程学报．1999，12(2)：173-181
[85] 周云，周福霖．桥梁震害与减震防灾新对策．世界地震工程．1997，13(1)：8-15
[86] 杨海荣，郑琦．日本公路桥的抗震鉴定和加固．国外桥梁．1997，2：69-77．82
[87] 欧进萍，吴波．弹塑性随机振动系统中恢复力学数学模型的若干形式．应用力学学报．1995，12(1)：63-70
[88] 杜修为．钢筋混凝土房屋结构弹塑性地震反应分析文献综述．世界地震工程．1990，4：1-7
[89] 薛伟辰，张志铁．钢筋混凝土结构非线性全过程分析方法及其应用．计算力学学报．1999，16(3)：334-342
[90] 刘南科，周基岳．钢筋混凝土框架的非线性全过程分析．土木工程学报．1990，23(4)：2-14
[91] 薛伟辰，吕志涛．混凝土杆系结构滞回全过程分析．工程力学．1996，13(3)：8-16
[92] 杜修力．结构弹塑性地震反应现状评述．工程力学．1994，11(2)：99-104
[93] 刘勇生．桥梁结构抗震研究的文献综述．世界地震工程．1992，1：48-55，62
[94] 王君杰．一般阻尼线性系统随机地震反应分析．工程力学．1994，11(4)：
109-114
[95] 田千里，关国雄，张佑启．具有滞迟耗能装置的高层建筑结构的随机响应分析．地震工程与工程振动．1995，15(2)：109-117
[96] 钱培风．高层建筑的抗震问题．世界地震工程．1992，3：15-21
[97] 刘庆华，徐虎．单柱式钢筋混凝土桥墩在水平地震作用下的损伤分析．工程力学．1997，3：108-112
[98] 胡世德，叶爱君．独柱式多层立交桥非线性地震反应分析．土木工程学报．1997，30(4)：19-25
[99] 周锡元，李中锡．规则型隔震桥梁结构的简化分析方法．土木工程学报．2001，34(3)：53-58，66
[100] 田琪，陈兴冲．拼装式桥墩接头的承载能力与滞回特性的试验研究．工程力学．1999，16(2)：107-113
[101] 章建军，刘进．兵库县南部地震中钢管桥墩损坏的数值模拟．国外桥梁．2000，2：59-64
[102] 严国敏．采用钢管加劲的混凝土组合结构高桥墩(之五)．国外桥梁．1999，1：45-47
[103] 李惠，王震宇．钢管高强混凝土叠合柱弯矩-曲率关系的合成模型．计算力学学报．2000，17(2)：184-191
[104] Y.Suzuki, R. Minai. A Method of Seismic Response Analysis of Hysteretic Structures Based on Stochastic Differential Equations. Proceedings of the Eighth World Conference on Earthquake Engnineering, San Francisco. 1984:459-466
[105] 赵雷．随机参数结构动力分析方法及地震可靠度研究．西南交通大学博士学位论文．1996
[106] 赵灿晖．大跨度钢管混凝土拱桥的地震响应研究．西南交通大学博士学位论文．2001
[107] 朱东生．桥梁抗震设计中几个问题的研究．西南交通大学博士学位论文．1999
[108] 陈兴冲．重力式桥墩-地基的线性及非线性动力性态研究．北方交通大学博士学位论文．1996
[109] 李乔．薄壁曲箱梁的空间分析理论．西南交通大学博士学位论文．1988
[110] K.J. Mθrk. Stochastic Response and Reliability Analysis of Hysteretic Structures. Ph.D. Thesis, university of ialborg,
Danmark. 1989
[111] G.Q. Cai, Y.K. Lin. Random Vibration of Strongly Nonlinear System. Journal of Nonlinear Dynamics. 2001, Vol. 24:3-15
[112] S. Erdal. Analysis of Earthquake Record from Structures:an Overview. NATO Advanced Research Workshop on Strong Motion Instrumentation for CivilEngineering Structures, Istanbul, Turkey. 1999:91-107
[113] S.F. Wojtkiewicz, L.A. Bergman, G. Turan. Covariance Control of a Hysteretic System. The 2nd World Conference on Structural Control, Kyoto, Japan. 1998:1967-1974
[114] Z.G. Ying, W.Q. Zhu, Y.Q. Ni, J.M. Ko. Stochastic Averaging of Duhem Hysteretic System. Journal of Sound and Vibration. 2OO2, Vol. 254:91-104
[115] M. Vasta, G.I. Schueller. Phase Space Reduction in Stochastic Dynamics. Journal of Engineering Mechanics. 2000, Vol. 126(6): 626-632
[116] Y.K. Lin, G.Q. Cai. Some Thoughts on Averaging Techniques in Stochastic Dynamics. Probabilistic Engineering Mechanic. 2000, Vol.15(1):7-14
[117] W.Q. Zhu, Z.G. Ying, Y. Suzuki. Optimal Nonlinear Feedback Control of Building Structures with AMD under Non-White Random Ground Acceleration Excitation. Internation Conference on Advances in Structural Dynamics. Hong Kong, China. 2000:13-15
[118] A. Elremaily. Seismic Behavior of High Strength Concrete Filled Tube(CFT)Columns. First International Conference on High Strength Concrete. Kona, Hawaii. 1997:13-18
[119] M. Shinozuka. Recent Developments in Stochastic Mechanics Relevant to Earthquake Engineering. Journal of Engineering Mechanics. 1996
[120] 铁道総合技术研究所．铁道构造物等设计标准·同解说-耐震设计．丸善株式会社．日本，东京．2000