大型复杂结构非平稳随机振动分析方法研究
|
摘要
现实世界充满偶然性,大到星体的产生、形成至毁灭的整个过程,小到生命个体的孕育、成长至死亡的整个过程。在自然科学技术领域,用随机性的观点对偶然性加以描述是大势所趋。对数学、物理或力学中的变量、场或过程用随机模型加以反映,就表述为随机变量、随机场或随机过程。把随机变量、随机场或随机过程与描述物理和工程振动问题的控制微分方程相结合就成了一个新的研究领域:随机动力微分方程。本文致力于大型复杂结构离散系统随机动力微分方程的求解。对于包含随机性的结构动力系统,其安全性能需要在概率意义上加以评估,结构动力可靠度分析是本文致力于研究的另外一个主要方面。
系数项为确定值、输入项为随机过程的随机动力微分方程所描述的物理问题就是通常所谓的经典随机振动问题,即确定性结构系统受随机激励作用的问题。功率谱法已经可以有效解决经典随机振动问题中的平稳随机振动问题。而对于非平稳随机振动问题,大型复杂结构随机振动的精确高效求解方法是目前的研究热点之一。根据线性结构输入与输出之间具有线性关系这一特点,在激励于离散时间间隔内随时间线性变化的假定下,推导了结构动力响应的显式表达式。依据动力响应的显式表达式,一方面可以根据矩的运算规律,直接计算结构响应的数字统计特征,提出了非平稳随机振动分析的时域显式直接法;另一方面可以实施蒙特卡罗模拟,利用数理统计方法计算结构响应的概率密度演化函数,提出了非平稳随机振动分析的时域显式随机模拟法。
对于系数项和输入项同时具有随机性的随机动力微分方程所描述的物理问题,通常称之为复合随机振动问题,即随机结构系统受随机激励作用的问题。已有的针对随机结构的随机振动分析方法各有优缺点,然而在工程应用中都未获推广。利用随机激励与结构随机参数之间具有相互独立性这一特点,采用分两步走的策略先后考虑激励随机性和结构参数随机性对随机响应的影响。以确定性结构随机振动分析的时域显式直接法为基础,以概率论中的条件数学期望为纽带,提出了随机结构非平稳随机振动分析的全数学期望法。
结构动力可靠度研究分为构件动力可靠度研究和体系动力可靠度研究两个层次。由于受到随机振动分析方法的限制,无论是确定性结构动力可靠度问题,还是随机结构动力可靠度问题,它们的研究仍停留在利用结构随机动力响应分析结果来计算结构动力可靠度的层次上,主要的研究基础并没有突破按照特殊跨越假定进行分析的格局。为克服已有动力可靠度计算方法的缺点,对于确定性结构,在动力响应显式表达式的基础上进行蒙特卡罗模拟以求解结构动力可靠度,提出了结构构件动力可靠度和体系动力可靠度分析的时域显式随机模拟法;对于随机结构,同样采用随机结构随机振动分析分两步走的策略,以确定性结构动力可靠度分析的时域显式随机模拟法为基础,以概率论中的条件概率为纽带,提出了随机结构构件动力可靠度和体系动力可靠度分析的全概率法。
前述随机振动分析方法和动力可靠度分析方法的计算效率取决于激励离散后时间截口随机变量的个数。为了进一步提高所提出方法的计算效率,把随机过程的KL分解(Karhunen-Loeve expansion)理论应用于随机激励的分解,提出了基于KL分解的确定性结构和随机结构的随机振动分析方法和动力可靠度分析方法。
理论方法的研究目的在于指导工程实践,并在工程实践中检验理论方法的有效性。新光大桥作为一种新型的、复杂的大跨度拱桥,由于结构的重要性、几何形状的特殊性、结构组成的多样性以及动力响应的复杂性,其抗震安全性能研究显得十分重要。利用本文提出的随机振动分析方法和动力可靠度分析方法,对新光大桥在非平稳地震作用下的随机响应和动力可靠度进行了分析。
数值算例和工程算例都表明本文所提出的随机振动分析方法和动力可靠度分析方法的精确性和高效性,它们为解决大型复杂结构的随机振动分析和动力可靠度分析提供了一条有效途径。
It is well acknowledged that the real world is full of contingency. This means that the lifetime of an astral body or a life being is a random process in nature. Therefore it is a general trend to describe the contingency from the randomness viewpoint in the field of natural science and technology. The variables, fields and processes associated with random models in mathematics, physics or mechanics could be represented by random variables, random fields and random processes, respectively. A new research field, the stochastic dynamic differential equations, emerges as vibration problems in physics and engineering are described by random variables, random fields and random processes. How to solve such equations of the discrete system of a large and complex structure is the focal point of this thesis. Besides, the research of this thesis also concentrates on the analysis of structural dynamic reliability, because the security of a dynamic system with random parameters has to be assessed in the sense of probability.
A problem described by a stochastic dynamic differential equation with deterministic coefficients and stochastic inputs of random processes, is the so-called classical random vibration problem, i.e. the problem of deterministic structures subjected to random excitations. Such problems have been studied intensively and solved efficiently by the power spectral method. However, for the problems of non-stationary random vibration analyses, especially for large and complex structures, seeking for an accurate and efficient method is still a research hotspot. In this thesis, explicit expressions in the time domain for dynamic responses of a structure are derived based on the linear relationship between the input and output of the linear structure and the assumption that the excitations vary linearly with time within a discrete time interval. Applying such explicit expressions, a direct formulation method in the time domain is proposed by which mean the values and variances of structure responses could be obtained directly according to the moment operation rules. Furthermore, a stochastic simulation method, termed as the explicit Monte-Carlo simulation method, is proposed by incorporating the derived explicit expressions to obtain the evolutionary probability functions of non-stationary responses.
The problems involving stochastic dynamic differential equations with stochastic coefficients and stochastic inputs are the so-called composite random vibration problems, in which the structure is stochastic and subjected to random excitations. The existing analysis methods for such problems have not yet been well accepted in engineering. In consideration of the mutual independence of randomness between structural parameters and excitation parameters, a strategy is adopted to reflect the influences of excitation parameters and structural parameters in two steps. By using the concept of conditional mathematical expectation in probability theory, a total mathematical expectation method for non-stationary random responses analysis of stochastic structures is proposed based on the direct formulation method for deterministic structures.
Dynamic reliability of a structure consists of two levels, the component dynamic reliability and the system dynamic reliability. Due to the limitation of existing random vibration analysis methods,the studies of dynamic reliability, no matter for deterministic structures or for stochastic structures, are still restricted by using particular excursion assumptions. In order to overcome these shortcomings, an explicit Monte-Carlo simulation method is proposed to analyze the component dynamic reliability and the system dynamic reliability of a deterministic structure based on explicit expressions of dynamic responses. Moreover, as to stochastic structures, the two-step strategy is also adopted and a total probability method is proposed based on the dynamic reliability analysis of deterministic structures and the concept of conditional probability in probability theory.
The computational efficiency of the proposed random vibration analysis methods and the dynamic reliability analysis methods depends on the number of random variables of excitations at discrete instants. Therefore, Karhunen-Loeve expansion theory is used to represent the random excitations in order to get higher computational efficiency. New random response analysis methods and dynamic reliability methods are proposed based on Karhunen-Loeve expansion theory.
To demonstrate the effectiveness of the proposed methods, the application of the present methods to the Xinguang Bridge is introduced as an example. A strict seismic safety evaluation is required for this new-style and complex large-span arch bridge due to the importance of the structure, the particular form of the geometry, the diversity of the structural composition and the complexity of the dynamic response. Random vibration analysis and dynamic reliability analysis of the Xinguang Bridge under non-stationary seismic excitations are conducted in this thesis.
Both numerical examples and engineering examples show good accuracy and efficiency of the proposed methods, indicating that such methods offer a novel and effective way to analyze the random vibration responses and dynamic reliabilities for large and complex structures.
系数项为确定值、输入项为随机过程的随机动力微分方程所描述的物理问题就是通常所谓的经典随机振动问题,即确定性结构系统受随机激励作用的问题。功率谱法已经可以有效解决经典随机振动问题中的平稳随机振动问题。而对于非平稳随机振动问题,大型复杂结构随机振动的精确高效求解方法是目前的研究热点之一。根据线性结构输入与输出之间具有线性关系这一特点,在激励于离散时间间隔内随时间线性变化的假定下,推导了结构动力响应的显式表达式。依据动力响应的显式表达式,一方面可以根据矩的运算规律,直接计算结构响应的数字统计特征,提出了非平稳随机振动分析的时域显式直接法;另一方面可以实施蒙特卡罗模拟,利用数理统计方法计算结构响应的概率密度演化函数,提出了非平稳随机振动分析的时域显式随机模拟法。
对于系数项和输入项同时具有随机性的随机动力微分方程所描述的物理问题,通常称之为复合随机振动问题,即随机结构系统受随机激励作用的问题。已有的针对随机结构的随机振动分析方法各有优缺点,然而在工程应用中都未获推广。利用随机激励与结构随机参数之间具有相互独立性这一特点,采用分两步走的策略先后考虑激励随机性和结构参数随机性对随机响应的影响。以确定性结构随机振动分析的时域显式直接法为基础,以概率论中的条件数学期望为纽带,提出了随机结构非平稳随机振动分析的全数学期望法。
结构动力可靠度研究分为构件动力可靠度研究和体系动力可靠度研究两个层次。由于受到随机振动分析方法的限制,无论是确定性结构动力可靠度问题,还是随机结构动力可靠度问题,它们的研究仍停留在利用结构随机动力响应分析结果来计算结构动力可靠度的层次上,主要的研究基础并没有突破按照特殊跨越假定进行分析的格局。为克服已有动力可靠度计算方法的缺点,对于确定性结构,在动力响应显式表达式的基础上进行蒙特卡罗模拟以求解结构动力可靠度,提出了结构构件动力可靠度和体系动力可靠度分析的时域显式随机模拟法;对于随机结构,同样采用随机结构随机振动分析分两步走的策略,以确定性结构动力可靠度分析的时域显式随机模拟法为基础,以概率论中的条件概率为纽带,提出了随机结构构件动力可靠度和体系动力可靠度分析的全概率法。
前述随机振动分析方法和动力可靠度分析方法的计算效率取决于激励离散后时间截口随机变量的个数。为了进一步提高所提出方法的计算效率,把随机过程的KL分解(Karhunen-Loeve expansion)理论应用于随机激励的分解,提出了基于KL分解的确定性结构和随机结构的随机振动分析方法和动力可靠度分析方法。
理论方法的研究目的在于指导工程实践,并在工程实践中检验理论方法的有效性。新光大桥作为一种新型的、复杂的大跨度拱桥,由于结构的重要性、几何形状的特殊性、结构组成的多样性以及动力响应的复杂性,其抗震安全性能研究显得十分重要。利用本文提出的随机振动分析方法和动力可靠度分析方法,对新光大桥在非平稳地震作用下的随机响应和动力可靠度进行了分析。
数值算例和工程算例都表明本文所提出的随机振动分析方法和动力可靠度分析方法的精确性和高效性,它们为解决大型复杂结构的随机振动分析和动力可靠度分析提供了一条有效途径。
It is well acknowledged that the real world is full of contingency. This means that the lifetime of an astral body or a life being is a random process in nature. Therefore it is a general trend to describe the contingency from the randomness viewpoint in the field of natural science and technology. The variables, fields and processes associated with random models in mathematics, physics or mechanics could be represented by random variables, random fields and random processes, respectively. A new research field, the stochastic dynamic differential equations, emerges as vibration problems in physics and engineering are described by random variables, random fields and random processes. How to solve such equations of the discrete system of a large and complex structure is the focal point of this thesis. Besides, the research of this thesis also concentrates on the analysis of structural dynamic reliability, because the security of a dynamic system with random parameters has to be assessed in the sense of probability.
A problem described by a stochastic dynamic differential equation with deterministic coefficients and stochastic inputs of random processes, is the so-called classical random vibration problem, i.e. the problem of deterministic structures subjected to random excitations. Such problems have been studied intensively and solved efficiently by the power spectral method. However, for the problems of non-stationary random vibration analyses, especially for large and complex structures, seeking for an accurate and efficient method is still a research hotspot. In this thesis, explicit expressions in the time domain for dynamic responses of a structure are derived based on the linear relationship between the input and output of the linear structure and the assumption that the excitations vary linearly with time within a discrete time interval. Applying such explicit expressions, a direct formulation method in the time domain is proposed by which mean the values and variances of structure responses could be obtained directly according to the moment operation rules. Furthermore, a stochastic simulation method, termed as the explicit Monte-Carlo simulation method, is proposed by incorporating the derived explicit expressions to obtain the evolutionary probability functions of non-stationary responses.
The problems involving stochastic dynamic differential equations with stochastic coefficients and stochastic inputs are the so-called composite random vibration problems, in which the structure is stochastic and subjected to random excitations. The existing analysis methods for such problems have not yet been well accepted in engineering. In consideration of the mutual independence of randomness between structural parameters and excitation parameters, a strategy is adopted to reflect the influences of excitation parameters and structural parameters in two steps. By using the concept of conditional mathematical expectation in probability theory, a total mathematical expectation method for non-stationary random responses analysis of stochastic structures is proposed based on the direct formulation method for deterministic structures.
Dynamic reliability of a structure consists of two levels, the component dynamic reliability and the system dynamic reliability. Due to the limitation of existing random vibration analysis methods,the studies of dynamic reliability, no matter for deterministic structures or for stochastic structures, are still restricted by using particular excursion assumptions. In order to overcome these shortcomings, an explicit Monte-Carlo simulation method is proposed to analyze the component dynamic reliability and the system dynamic reliability of a deterministic structure based on explicit expressions of dynamic responses. Moreover, as to stochastic structures, the two-step strategy is also adopted and a total probability method is proposed based on the dynamic reliability analysis of deterministic structures and the concept of conditional probability in probability theory.
The computational efficiency of the proposed random vibration analysis methods and the dynamic reliability analysis methods depends on the number of random variables of excitations at discrete instants. Therefore, Karhunen-Loeve expansion theory is used to represent the random excitations in order to get higher computational efficiency. New random response analysis methods and dynamic reliability methods are proposed based on Karhunen-Loeve expansion theory.
To demonstrate the effectiveness of the proposed methods, the application of the present methods to the Xinguang Bridge is introduced as an example. A strict seismic safety evaluation is required for this new-style and complex large-span arch bridge due to the importance of the structure, the particular form of the geometry, the diversity of the structural composition and the complexity of the dynamic response. Random vibration analysis and dynamic reliability analysis of the Xinguang Bridge under non-stationary seismic excitations are conducted in this thesis.
Both numerical examples and engineering examples show good accuracy and efficiency of the proposed methods, indicating that such methods offer a novel and effective way to analyze the random vibration responses and dynamic reliabilities for large and complex structures.
引文
[1.1]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[1.2]朱位秋.随机振动[M].北京:科学出版社,1992
[1.3]张森文,庄表中,欧阳怡,等.我国随机振动研究近10年来的进展[J].振动与冲击,1997,16(3):1-8
[1.4] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal, 1944, 23(3): 282-332
[1.5] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal, 1945, 24(1): 46-156
[1.6] Crandall S H.Random vibration [M].Massachusetts: The MIT Press, 1958
[1.7] Crandall S H, Mark W D.Random vibration in mechanical systems [M].New York: Academic Press, 1963
[1.8] Lin Y K.Probabilistic theory of structural dynamics [M].New York: McGraw-Hill, 1967
[1.9]星谷胜.随机振动分析[M].常宝琦(译).北京:地震出版社,1977
[1.10] Nigam N C.Introduction to random vibration [M].Massachusetts: MIT Press, 1983
[1.11] Newland D E . An introduction to random vibrations and spectral analysis [M].Second edition.London: Longman, 1984
[1.12]季文美,方同,陈松淇.机械振动[M].北京:科学出版社,1985
[1.13]庄表中,陈乃立,高瞻.非线性随机振动理论及应用[M].杭州:浙江大学出版社,1986
[1.14] Yang C Y.Random vibration of structures [M].New York: John Wiley & Sons, 1986
[1.15] Roberts J B, Spanos P D.Random vibration and statistical linearization [M].New York: John Wiley & Sons, 1990
[1.16] Lin Y K, Cai G Q . Probabilistic structural dynamics: advanced theory and applications [M].New York: McGraw-Hill Press, 1995
[1.17] Wirsching P H , Paez T L, Ortiz K.Random vibrations: theory and practice [M].New York: John Wiley & Sons, 1995
[1.18]方同.工程随机振动[M].北京:国防工业出版社,1995
[1.19] Lutes L D, Sarkani S.Stochastic analysis of structural and mechanical vibration [M].New Jersey: Prentice-Hall, 1997
[1.20]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998
[1.21] Lutes L D, Sarkani S.Random vibrations: analysis of structural and mechanical systems [M].Burlington: Elsevier Butterworth-Heinemann, 2004
[1.22]张柄根,赵玉芝.科学与工程中的随机微分方程[M].北京:海洋出版社,1980
[1.23]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007
[1.24]张琳琳.随机风场研究与高耸、高层结构抗风可靠性分析[D].上海:同济大学,2006
[1.25]林家浩,钟万勰,张文首.结构非平稳随机响应方差矩阵的直接精细积分计算[J].振动工程学报,1999,12(1): 1-8
[1.26]孙作玉,王晖.结构非平稳随机响应方差数值计算方法[J].振动工程学报,2009,22(3):325-328
[1.27] Hoshiya M, Ishii K, Nagata S.Recursive covariance of structural responses [J].Journal of Engineering Mechanics,1984,110(12): 1743-1755
[1.28] To C W S.A stochastic version of the Newmark family of algorithms for discretized dynamic systems [J].Computers and Structures, 1992, 44(33): 667-673
[1.29] To C W S, Liu M L.Recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom non-linear system [J].Computers and Structures, 1993, 48(6): 993-1000
[1.30] Miao B Q.Direct integration variance prediction of random response of nonlinear systems [J].Computers and Structures, 1993, 46(6): 979-983
[1.31]缪炳祺,胡夏夏,许礼深.结构非平稳随机响应分析的Newmark递推算法[J].强度与环境,1996,23(1):34-39
[1.32] Tootkaboni M, Graham-Brady L.Stochastic direct integration schemes for dynamic systems subjected to random excitations [J].Probabilistic Engineering Mechanics, 2010, 25(2): 163-171
[1.33]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
[1.34]朱位秋.非线性随机动力学与控制[M].北京:科学出版社,2003
[1.35] Thomas K, Caughey T.Equivalent linearization techniques [J].Journal of the Acoustical Society of America, 1963, 35(11): 1706-1711
[1.36] Atalik T S, Utku S.Stochastic linearization of mufti-degree-of freedom non-linear systems [J].Earthquake Engineering and Structural Dynamics, 1976, 4(4): 411-420
[1.37] Spanos P D.Stochastic linearization in structural dynamics [J].Applied Mechanics Review, 1981, 34(1): 1-8
[1.38] Zhu W Q.Stochastic averaging methods in random vibration [J].Applied Mechanics Reviews, 1988, 41(5): 189-199
[1.39]陈建兵.随机结构非线性反应概率密度演化分析[D].上海:同济大学,2002
[1.40] Ghanem R G, Spanos P D.Stochastic finite element: a spectral approach [M].New York: Springer-Verlag, 1991
[1.41] Kleiber M, Hien T D.The stochastic finite element method: basic perturbation technique and computer implementation [M].New York: John Wiley & Sons, 1992
[1.42]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[1.43] Giovanni F, Gabriele F.A dynamic stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures [J].Structural Engineering and Mechanics, 2006, 23(6): 599-613
[1.44]车建文.基于可靠性的结构动力优化设计研究[D].西安:西安电子科技大学,1998
[1.45]高伟.随机、智能结构随机振动分析与主动控制研究[D].西安:西安电子科技大学,2003
[1.46]雒卫廷.基于完全概率的随机结构分析与可靠性研究[D].西安:西安电子科技大学,2007
[1.47] Li J, Chen J B.Stochastic dynamics of structures [M].New York: John Wiley & Sons, 2009
[1.48] Shinozuka M.Monte Carlo solution of structural dynamics [J].Computers and Structures, 1972, 2(5): 855-874
[1.49] Shinozuka M, Jan C M.Digital simulation of random processes and its applications [J].Journal of Sound and Vibration, 1972, 25(1): 111-128
[1.50] Shinozuka M, Wen Y K.Monte Carlo solution of nonlinear vibration [J].AIAA Journal, 1972, 10(1): 37-40
[1.51] Astill C J, Noisseir S B, Shinozuka M.Impact loading on structures with random properties [J].Journal of Structural Mechanics, 1972, 1(1): 63-67
[1.52] Sun T C.A finite element method for random differential equations with random coefficients [J].Journal of Numerical Analysis, 1979, 16(6): 1019-1035
[1.53] Jensen H, Iwan W D.Response variability in structural dynamics [J].Earthquake Engineering and Structural Dynamics, 1991, 20(10): 949-959
[1.54] Jensen H, Iwan W D.Response of systems with uncertain parameters to stochastic excitation [J].Journal of Engineering Mechanics, 1992, 118(11): 1012-1025
[1.55] Iwan W D, Jensen H.On the dynamic response of continuous systems including model uncertainty [J].Journal of Applied Mechanics, 1993, 60(2): 484-490
[1.56]李杰.随机结构分析的扩阶系统方法(I)-扩阶系统方程[J].地震工程与工程振动,1995,15(3):111-118
[1.57]李杰.随机结构分析的扩阶系统方法(II)-结构动力分析[J].地震工程与工程振动,1995,15(4):27-35
[1.58]李杰.复合随机振动分析的扩阶系统方法[J].力学学报,1996,28(1):66-75
[1.59] Dostupov B G, Pugachev V S.The equation for the integral of a system of ordinary differential equations containing random parameters [J].Automatika i Telemekhanika, 1957, 18(4): 620-630
[1.60] Ding G Y, Li J.The nonlinear response emulation analysis of stochastic structure subjected to the earthquake excitation [A].New Zealand: The 12th World Earthquake Engineering Conference, 2000
[1.61]丁光莹.钢筋混凝土框架结构非线性反应分析的数值模拟分析[D].上海:同济大学,2001
[1.62] Liu W K, Belytschko T, Mani A.Probabilistic finite elements for nonlinear structural dynamics [J].Computer Methods in Applied Mechanics and Engineering, 1986, 56(1) 61-81
[1.63] Ma A J, Chen S H, Han W Z.Stochastic properties of response for nonlinear structural systems with random parameters [J].Computers and Structures, 1996, 58(6): 1139-1144
[1.64] Klosner J M, Haber S F, Voltz P.Response of non-linear systems with parameter uncertainties [J].International Journal of Non-linear Mechanics, 1992, 27(4): 547-563
[1.65] Bernard P, Wu L M.Stochastic linearization: the theory [J].Journal of Applied Probability 1998, 35(3): 718-730
[1.66] Bernard P.Stochastic linearization: what is available and what is not [J].Computers and Structures, 1998, 67(1): 9-18
[1.67] Zielihski A P, Frey F.On linearization in non-linear structural finite element analysis [J].Computers and Structures, 2001, 79(8): 825-838
[1.68] Anders M, Hori M . Three-dimensional stochastic finite element method for elastic-plastic bodies [J].International Journal for Numerical Methods in Engineering, 2001, 51(4): 449-478
[1.69]钟万勰.一个高效结构随机响应算法系列-虚拟激励法[J].自然科学进展,1996,6(4):394-401
[1.70] Lin J H.Zhao Y, Zhang Y H.Accurate and highly efficient algorithms for structural stationary/non-stationary random responses [J].Computer Methods in Applied Mechanics and Engineering, 2001, 9(1): 103-111
[1.71] Bathe K J.Finite element procedures [M].New Jersey: Prentice-Hall, 1996
[1.72] Yamazaki F, Shinozuka M, Dasgupta G.Neumann expansion for stochastic finite element analysis [J].Journal of Engineering Mechanics, 1988, 114(8): 1335-1345
[1.73]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].成都:西南交通大学,1996
[1.74] Chakraborty S, Dey S S.A stochastic finite element dynamic analysis of structures with uncertain parameters [J].International Journal of Mechanical Sciences, 1998, 40(11): 1071-1087
[1.75]赵雷,陈虬.随机有限元动力分析方法的研究进展[J].力学进展,1999,29(1):9-18
[1.76] Liu W K, Besterfield G, Belytschko T.Transient probabilistic systems [J].Computer Methods in Applied Mechanics and Engineering, 1988, 67(1): 27-54
[1.77]林家浩,夏杰,张亚辉,等.非平稳随机摄动分析中的久期项效应[J].振动工程学报,2003,16(1):124-128
[1.78] Wang F Y, Zhao Y, Lin J H.Stochsatic response analysis of structures with random properties subjected to stationary random excitation[C].Earth and space2010: Engineering, Science, Construction, and Operation in Challenging Environments, 2010, 2949-2957
[1.79]王凤武,楼梦麟.随机参数结构体系的随机地震响应计算方法[J].同济大学学报,2004,32(1):6-9
[1.80] Sniady P, Adamowski R, Kogut G, et al.Spectral stochastic analysis of structures with uncertain parameters [J].Probabilistic Engineering Mechanics, 2008, 23(1): 76-83
[1.81] Ghanem R, Spanos P D.Polynomial chaos in stochastic finite elements [J].Journal of Applied Mechanics, 1990, 57(1): 197-202
[1.82]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3):263-267
[1.83]李杰,廖松涛.线性随机结构在随机激励下动力响应分析[J].力学学报,200,34(3):416-424
[1.84]胡太彬,陈建军,王小兵,等.不均匀随机参数桁架结构的随机反应分析[J].工程力学,2007,24(2):126-131
[1.85]胡太彬,陈建军,徐亚兰.随机参数平面刚架结构频率特性分析的随机因子法[J].机械强度,2006,28(2):196-200
[1.86] Gao W, Chen J J, Ma H B.Dynamic response analysis of closed loop control system for intelligent truss structures based on probability [J].Structural Engineering and Mechanics, 2003, 15(2): 239-248
[1.87]高伟,陈建军.线性随机结构的平稳随机响应分析[J].应用力学学报,2003,20(3):92-95
[1.88] Gao W, Chen J J, Ma J, et al. Dynamic response analysis of stochastic frame structures under nonstationary random excitation [J].AIAA Journal, 2004, 42(9): 1818-1822
[1.89] Gao W, Chen J J, Cui M T, et al.Dynamic response analysis of linear stochastic truss structures under stationary random excitation [J].Journal of Sound and Vibration, 28(2): 311-321
[1.90] Syski R.Stochastic differential equations [M].New York: McGraw-Hill, 1967
[1.91] Fuller A T.Analysis of nonlinear stochastic systems by means of the Fokker-Planck equation [J].International Journal of Control, 1969, 9(6): 603-655
[1.92]李杰,陈建兵.随机动力系统中的广义密度演化方程[J].自然科学进展,2006,16(6):712-719
[1.93] Chen J B, Li J.A note on the principle of preservation of probability and probability density evolution equation [J].Probabilistic Engineering Mechanics, 2009, 24(1): 51-59
[1.94]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[J].北京:地震出版社,1993
[1.95]李桂清,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001
[1.96]陈建兵,李杰.随机机构动力可靠度分析的极值概率密度函数[J].地震工程与工程振动,2004,24(6):39-44
[1.97]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121-125
[1.98]李桂青,曹宏.动力可靠性评述[J].地震工程与工程振动,1983,3(3):42-62
[1.99]欧进萍.国外动力可靠性理论述评[J].武汉建材学院学报,1983,5(2):231-248
[1.100] Coleman J J.Reliability of aircraft structures in resisting chance failure operations [J].Operations Research, 1959, 7(4): 639–645
[1.101] Crandall S H.First crossing probabilities of the linear oscillator [J].Journal of Sound and Vibration, 1970, 12(3): 285-299
[1.102] Yang J N, Shinozuka M.On the first excursion probability in stationary narrow-band random vibration [J].Journal of Applied Mechanics, 1971, 38(4): 1017-1022
[1.103] Yang J N, Shinozuka M.On the first excursion probability in stationary narrow band random vibration-2 [J].Journal of Applied Mechanics, 1972, 39(3): 733-738
[1.104] Yang Y N.Nonstationary envelop process and first excursion probability [J].Journal of Structural Mechanics, 1972, 1(2): 231-248
[1.105] Yang Y N.First excursion probability in nonstationary random vibration [J].Journal of Applied Mechanics, 1973, 26(3): 417-428
[1.106] Madsen H O, Krenk S, Lind N C.Methods of structural safety [M].New Jersey: Prentice-Hall, 1986
[1.107] Roberts J B.An approach to the first-passage problem in random vibration [J].Journal of Sound and Vibration, 1968, 8(2): 301-328
[1.108] Cramer H.On the intersections between the trajectories of a normal stationary stochastic process and a high level [J].Arkiv for Matematik, 1966, 6(2): 337-349
[1.109] Corotis R B, Vanmarcke E H, Cornell C A.First passage of nonstationary random processes[J].Journal of the Engineering Mechanics Division, 1972, 98(2): 401–414
[1.110] Vanmarcke E H.On the distribution of the first-passage time for normal stationary random processes [J].Journal of Applied Mechanics, 1975, 42(2): 215-220
[1.111]李杰,陈建兵.概率密度演化方程-历史、进展与应用[M].上海:同济大学,2008
[1.112] Park B T.Petrosian V.Fokker-Planck equations of stochastic acceleration: a study of numerical method [J].The Astrophysical Journal Supplement Series, 1996, 103(1): 255-267
[2.1] Gasparini D A.Response of MDOF systems to non-stationary random excitation [J].Journal of Engineering Mechanics Division, 1979, 105(1): 13-27
[2.2]王超,徐晖,高耀南,等.非平稳激励下结构动力可靠度计算[J].西安交通大学学报,1993,27(4):47-52
[2.3]肖梅玲,高春涛,叶燎原.结构地震反应在小波基下的动力可靠性分析[J].世界地震工程,2002,18(1):27-33
[2.4] Chaudhuri A, Chakraborty S.Reliability evaluations of 3-D frame subjected to non-stationary earthquake [J].Journal of Sound and Vibration, 2003, 259(4): 797-808
[2.5]石少卿,姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究[J].应用力学学报,1999,16(4):73-77
[2.6]曹晖,赖明,白绍良.基于小波分析的结构动力可靠度估计[J].世界地震工程,2000,16(4):70-77
[2.7] Au S K, Beck J L.First excursion probabilities for linear systems by very efficient importance sampling [J].Probabilistic Engineering Mechanics, 2001, 16(3): 193-207
[2.8] Pradlwarter H J, Schueller G I.Excursion probabilities of non-linear systems [J].International Journal of Non-linear Mechanics, 2004, 39(9): 1447-1452
[2.9] Pradlwarter H J, Schueller G I, Koutsourelakis P S, et al.Application of line sampling simulation method to reliability benchmark problems [J].Structural Safety, 2007,29(3): 208-221
[2.10] Au S K, Beck J L.Estimation of small failure probabilities in high dimensions by subset simulation [J].Probabilistic Engineering Mechanics, 2001, 16(4): 263-277
[2.11] Ching J, Beck J L, Au S K.Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation [J].Probabilistic Engineering
Mechanics, 2005, 20(3): 199-214
[2.12] Au S K, Ching J, Beck J L.Application of subset simulation methods to reliability benchmark problems [J].Structural Safety, 2007, 29(3): 183-193
[2.13] Priestley M B.Evolutionary spectral and non-stationary process [J].Journal of Royal Statistical Society, 1965, 27(2): 204-237.
[2.14] Priestley M B.Power spectral analysis of non-stationary random process [J].Journal of Sound and Vibration, 1967, 6(1): 86-97
[2.15] Priestly M B.Spectral analysis and time series [M].London: Academic Press, 1981
[2.16] Mark W D.Spectral analysis of the convolution and filtering of non-stationary stochastic processes [J].Journal of Sound and Vibration, 1970, 11(1): 19-63
[2.17] Mark W D.Characterization of stochastic transients and transmission media: the method of power-moments spectra [J].Journal of Sound and Vibration, 1972, 22(3): 249-295
[2.18] Loynes R M.On the concept of the spectrum for nonstationary processes [J].Journal of Royal Statistical Society, 1968, 30(1): 1-30
[2.19] Eberly J H, Wodkiewicz K.The time-dependent physical spectrum of light [J].Journal of the Optical Society of America, 1977, 67(9): 1252-1261
[2.20]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
[2.21]李英民,赖明.工程地震动模型化研究综述及展望(Ⅱ)-平稳模型及均匀调制过程[J].重庆建筑大学学报,1998,20(4):111-118
[2.22]李英民,赖明.工程地震动模型化研究综述及展望(Ⅲ)-其它工程学模型与展望[J].重庆建筑大学学报,1998,20(5):108-114
[2.23]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136
[2.24]朱位秋.随机振动[M].北京:科学出版社,1992
[2.25] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal,1944, 23(3): 282-332
[2.26] Shinozuka M.Simulation of multivariate and multidimensional random processes [J].Journal of the Acoustical Society of America, 1971, 49(1): 357-368
[2.27] Iannuzzi A, Spinelli P.Artificial wind generation and structural response [J].Journal of Structural Engineering, 1987, 113(12): 2382-2398
[2.28] Saul W E, Jayachandran P, Peyrot A H.Response to stochastic wind of N-degree tall buildings [J].Journal of Structural Engineering, 1976, 102(5): 1059-1075
[2.29] Mignolet M P, Spanos P D.MA to ARMA modeling of wind [J].Journal of Wind Engineering and Industrial Aerodynamics, 1990, 36(1-3): 429-438
[2.30] Mignolet M P, Spanos P D.Optimality in the estimation of a MA system from a long AR model for simulation studies [J].Soil Dynamics and Earthquake Engineering, 1995, 14(6): 445-452
[2.31] Mignolet M P, Spanos P D.A direct determination of ARMA algorithms for the simulation of stationary random processes [J].International Journal of Non-Linear Mechanics, 1990, 25(5): 555-568
[2.32] Saramas E, Shinozuka M.ARMA representation of random processes [J].Journal of Engineering Mechanics, 1985, 111(3): 449-461
[2.33] Shinozuka M, Sato Y.Simulation of nonstationary random process [J].Journal of Engineering Mechanics, 1967, 63(1): 11-40
[2.34] Deodatis G, Shinozuka M.Autoregressive model for non-stationary stochastic process [J].Journal of Engineering Mechanics, 1988, 114(11): 1995-2012
[2.35] Li Y S, Kareem A.Simulation of multivariate nonstationary random process by FFT [J].Journal of Engineering Mechanics, 1991, 117(5): 1037-1058
[2.36] Grigoriu M.Simulation of nonstationary gaussian processes by random trigonometric polynomials [J].Journal of Engineering Mechanics, 1993, 119(2): 328-343
[2.37] Deodatis G.Non-stationary stochastic vector processes: seismic ground motion applications [J].Probabilistic Engineering Mechanics, 1996, 11(3): 149-168
[2.38] Li Y S, Kareem A.Simulation of multivariate nonstationary random processes: Hybrid DFT and digital filtering approach [J].Journal of Engineering Mechanics, 1997,
123(12): 1302-1310
[2.39]杨庆山,姜海鹏,陈英俊.基于相位差谱的时-频非平稳人造地震动的生成[J].地震工程与工程振动,2001,21(3):10-16
[2.40]张建仁,刘扬,许福友,郝海霞.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
[2.41] Cressie N.Statistics for Spatial Data [M].New York: John Wiley & Sons, 1993
[2.42]陈太聪.结构工程自适应控制的参数分析新方法研究及其在大跨度斜拉桥施工中的应用[D].广州:华南理工大学,2003
[2.43]林家浩,钟万勰,张亚辉.大跨度结构抗震计算的随机振动分析方法[J].建筑结构学报,2000,21(1):29-36.
[2.44]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用[M].北京:地震出版社,1993
[2.45]李桂清,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001
[2.46] Nowak A S, Collins K R.Reliability of Structures [M].New York: McGraw-Hill, 2000
[2.47] Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion [J].Bulletin of the Earthquake Research Institute, University of Tokyo, 1957, 35(2): 308-325
[2.48]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21-26
[3.1]李杰.结构动力分析的若干发展趋势[J].世界地震工程,1993,8(2):1-8
[3.2] Shinozuka M.Monte Carlo solution of structural dynamics [J].Computers andStructures, 1972, 2(5): 855-874
[3.3] Shinozuka M, Jan C M.Digital simulation of random processes and its applications [J].Journal of Sound and Vibration, 1972, 25(1): 111-128
[3.4] Shinozuka M, Wen Y K.Monte Carlo solution of nonlinear vibration [J].AIAA Journal, 1972, 10(1): 37-40
[3.5] Astill C J, Noisseir S B, Shinozuka M.Impact loading on structures with random properties [J].Journal of Structural Mechanics, 1972, 1(1): 63-67
[3.6] Ghanem R G, Spanos P D.Stochastic finite element: a spectral approach [M].New York: Springer-Verlag, 1991
[3.7] Kleiber M, Hien T D.The stochastic finite element method: basic perturbation technique and computer implementation [M].New York: John Wiley & Sons, 1992
[3.8]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[3.9]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[3.10] Giovanni F, Gabriele F.A dynamic stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures [J].Structural Engineering and Mechanics, 2006, 23(6): 599-613
[3.11]车建文.基于可靠性的结构动力优化设计研究[D].西安:西安电子科技大学,1998
[3.12]高伟.随机、智能结构随机振动分析与主动控制研究[D].西安:西安电子科技大学,2003
[3.13]雒卫廷.基于完全概率的随机结构分析与可靠性研究[D].西安:西安电子科技大学,2007
[3.14] Li J, Chen J B.Stochastic dynamics of structures [M].New York: John Wiley & Sons, 2009
[3.15]曹宏,李秋胜,李芝艳.随机结构动力反应和可靠性分析[J].应用数学和力学,1993,14(10):931-938
[3.16]胡太彬,陈建军,高伟,马娟.平稳随机激励下随机桁架结构动力可靠性分析[J].力学学报,2004,36(2):241-246
[3.17] Spencer B F Jr, Elishakoff I . Reliability of uncertain linear and nonlinear systems[J].Journal of Engineering Mechanics, 1988, 114(1): 135-149
[3.18] Papadimitriou C, Beck J L, Katafydiotis L S.Asymptotic expansions for reliability and moments of uncertain systems [J].Journal of Engineering Mechanics, 1997, 123(12): 1219-1229
[3.19]乔红威,吕震宙.非平稳随机激励下随机结构的动力可靠性分析[J].固体力学学报,2008,29(1):36-40
[3.20]乔红威,吕震宙,关爱锐,刘旭华.平稳随机激励下随机结构动力可靠度分析的多项式逼近法[J].工程力学,2009,26(2):60-64
[3.21] Brenner C E, Bucher C.A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading [J].Probabilistic Engineering Mechanics, 1995, 10(4): 265-273
[3.22]陈颖,王东升,朱长春.随机结构在随机载荷下的动力可靠度分析[J].工程力学,2006,23(10):82-85
[3.23]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121-125
[3.24]陈建兵,李杰.复合随机振动系统的动力可靠度分析[J].工程力学,2005,22(3):52-57
[3.25] Li J, Chen J B, Fan W L.The equivalent extreme-value event and evaluation of the structural system reliability [J].Structural Safety, 2007, 29(1): 112-131
[3.26] Bucher C G, Bourgund U.A fast and efficient response surface approach for structural reliability problems [J].Structural Safety, 1990, 7(1): 57-66
[3.27] Chaudhuri A, Chakraborty S . Reliability of linear structures with parameter uncertainty under non-stationary earthquake [J].Structural Safety, 2006, 28(3): 231-246
[3.28] Zhao Y G, Ono T, Idota H.Response uncertainty and time-variant reliability analysis for hysteretic MDF structures [J].Earthquake Engineering and Structural Dynamics, 1999, 28(10): 1187-1213
[3.29] Zhao Y G, Ono T.New point estimates for probability moments [J].Journal of Engineering Mechanics, 2000, 126(4): 433-436
[3.30]王梓坤.概率论基础及其应用[M].北京:北京师范大学出版社,2007
[3.31]严士健,王隽骧,刘秀芳.概率论基础[M].北京:科学出版社,2009
[4.1] Karhunen K.Uber lineare methoden in der wahrscheinlichkeitsrechnung [M].Annales Academiae Scientiarum Fennicae(Series A1): Mathematica-Physica, 1947
[4.2] Loeve M.Probability theory [M].Berlin: Springer-Verlag, 1977
[4.3] Lumley J L.Stochastic tools in turbulence[M].London: Academic Press, 1970
[4.4]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[4.5] Solari G, Carassale L, Tubino F.Proper orthogonal decomposition in wind engineering. Part 1: A state-of-art and some prospects[J].Wind and Structures, 2007, 10(2): 153-176
[4.6] Carassale L, Solari G, Tubino F.Proper orthogonal decomposition in wind engineering. Part 2: Theoretical aspects and some application[J].Wind and Structures, 2007,10(2): 177-208
[4.7] Grigoriu M.Evaluation of Karhunen-Loeve, Spectral, and Sampling Representations for Stochastic Processes [J].Journal of Engineering Mechanics, 2006, 132(2): 179-189
[4.8] Feeny B F, Kappagantu R.On the physical interpretation of proper orthogonal modes in vibrations[J]. Journal of Sound and Vibration, 1998, 211(44): 607-616
[4.9] Ravindra B.Comments on“On the physical interpretation of proper orthogonal modes in vibrations”[J].Journal of Sound and Vibration, 1999, 219(1): 189-192
[4.10] Van Trees H I.Detection, estimation and modulation theory: Part 1 [M]. New York: John Wiley & Sons, 1968
[4.11]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007
[4.12] Phoon K K, Huang S P, Quek S T.Implementation of Karhunen-Loeve expansion for simulation using wavelet-Galerkin scheme[J].Probabilistic Engineering Mechanics, 2002, 17(3): 293-303
[4.13] Phoon K K, Huang H W, Quek S T.Comparison between Karhunen-Loeve and wavelet expansions for simulation of Gaussian processes[J].Computers and Structure,2004, 82(5): 985-991
[4.14] Zhang J, Ellingwood B.Orthogonal series expansions of random fields in reliability analysis[J].Journal of Engineering Mechanics, 1994, 120(12): 2660-2667
[4.15]刘天云,伍朝晖,赵国藩.随机场的投影展开法[J].计算力学学报,1997,14(4):484-489
[4.16]李杰,刘章军.基于标准正交基的随机过程展开法[J].同济大学学报,2006,36(10):1279-1282
[4.17]刘章军,李杰.脉动风速随机过程的正交展开[J].振动工程学报,2008,21(1):96-101
[4.18]李杰,刘章军.随机脉动风场的正交展开法[J].土木工程学报,2008,41(2):49-53
[4.19] Phoon K K, Quek S T, Huang H W.Simulation of non-Gaussian processes using fractile correlation[J].Probabilistic Engineering Mechanics, 2004, 19(4): 287-292
[4.20] Phoon K K, Huang H W, Quek S T.Simulation of strongly non-Gsussian processes using Karhunen-Loeve expansion [J].Probablisitic Engineering Mechanics, 2005, 20(2): 188-198
[4.21] Li L B, Phoon K K, Quek S T.Comparison between Karhunen-Loeve expansion and translation-based simulation of non-Gaussian processes [J]. Computers and Structures, 2007, 85(5-6): 264-276
[4.22]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
[5.1]李国豪.工程结构抗震动力学[M].上海:科学技术出版社,1980
[5.2] Housner G W.Characteristic of strong motion earthquakes [J].Bulletin of the Seismological Society of America, 1947, 37(1): 17-31
[5.3] Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion [J].Bulletin of the Earthquake Research Institute, University of Tokyo, 1957, 35(2):308-325
[5.4]胡聿贤,周锡元.弹性体系在平稳和平稳化地面运动下的反应[M].中国科学院土木建筑研究所地震工程研究报告集(第1集).北京:科学出版社,1962:33-50
[5.5] Clough R W, Penzien J.Dynamics of structures [M].New York: McGraw-Hill, 1993
[5.6]欧进萍,牛荻涛.地震地面运动随机模型的参数及其结构效应[J].哈尔滨建筑工程学院学报,1990,10(2):70-76
[5.7]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5
[5.8]李英明,刘立平,赖明.工程地震动随机功率谱模型的分析与改进[J].2008,25(3):43-48
[5.9]范立础,胡世德,叶爱君.大跨度桥梁抗震设计[M].北京:人民交通出版社,2001
[5.10]陈海斌.大跨度桥梁非线性抗震分析[D].广州:华南理工大学,2006
[5.11]徐升桥,任为东,彭岚平,等.广州市新光快速路工程新光大桥施工图设计[Z].北京:铁道部专业设计院,2004
[5.12]谭林.基于动力指纹的结构损伤识别可靠度方法研究[D].广州:华南理工大学,2010
[5.13] Amin M, Ang A H S.Nonstationary stochastic model of earthquake motion [J].Engineering Mechanics Division, 1968, 94(2): 559-584
[5.14]李英民,赖明.工程地震动模型化研究综述及展望(II)-平稳模型及均匀调制过程[J].重庆建筑大学学报,1998,20(4):111-118
[5.15]广东省地震工程勘测中心.广州新光快速路工程场地地震安全性评价报告.2003
[5.16]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10
[5.17]田利,李宏男.基于《电力设施抗震设计规范》的地震动随机模型参数研究[J].防灾减灾工程学报,2010,30(1):17-22
[5.18]李跃,张健峰,卢汝生,等.广州新光大桥[M].北京:人民交通出版社,2009
[5.19]朱伯龙,董振祥.钢筋混凝土非线性分析[M].上海:同济大学出版社,1985
[5.20] Mander J B, Priestley M J N,Park R.Theoretical stress-strain model for confined concrete [J].Journal of Structural Engineering, 1988, 114(8): 1804-1826
[1.2]朱位秋.随机振动[M].北京:科学出版社,1992
[1.3]张森文,庄表中,欧阳怡,等.我国随机振动研究近10年来的进展[J].振动与冲击,1997,16(3):1-8
[1.4] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal, 1944, 23(3): 282-332
[1.5] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal, 1945, 24(1): 46-156
[1.6] Crandall S H.Random vibration [M].Massachusetts: The MIT Press, 1958
[1.7] Crandall S H, Mark W D.Random vibration in mechanical systems [M].New York: Academic Press, 1963
[1.8] Lin Y K.Probabilistic theory of structural dynamics [M].New York: McGraw-Hill, 1967
[1.9]星谷胜.随机振动分析[M].常宝琦(译).北京:地震出版社,1977
[1.10] Nigam N C.Introduction to random vibration [M].Massachusetts: MIT Press, 1983
[1.11] Newland D E . An introduction to random vibrations and spectral analysis [M].Second edition.London: Longman, 1984
[1.12]季文美,方同,陈松淇.机械振动[M].北京:科学出版社,1985
[1.13]庄表中,陈乃立,高瞻.非线性随机振动理论及应用[M].杭州:浙江大学出版社,1986
[1.14] Yang C Y.Random vibration of structures [M].New York: John Wiley & Sons, 1986
[1.15] Roberts J B, Spanos P D.Random vibration and statistical linearization [M].New York: John Wiley & Sons, 1990
[1.16] Lin Y K, Cai G Q . Probabilistic structural dynamics: advanced theory and applications [M].New York: McGraw-Hill Press, 1995
[1.17] Wirsching P H , Paez T L, Ortiz K.Random vibrations: theory and practice [M].New York: John Wiley & Sons, 1995
[1.18]方同.工程随机振动[M].北京:国防工业出版社,1995
[1.19] Lutes L D, Sarkani S.Stochastic analysis of structural and mechanical vibration [M].New Jersey: Prentice-Hall, 1997
[1.20]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998
[1.21] Lutes L D, Sarkani S.Random vibrations: analysis of structural and mechanical systems [M].Burlington: Elsevier Butterworth-Heinemann, 2004
[1.22]张柄根,赵玉芝.科学与工程中的随机微分方程[M].北京:海洋出版社,1980
[1.23]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007
[1.24]张琳琳.随机风场研究与高耸、高层结构抗风可靠性分析[D].上海:同济大学,2006
[1.25]林家浩,钟万勰,张文首.结构非平稳随机响应方差矩阵的直接精细积分计算[J].振动工程学报,1999,12(1): 1-8
[1.26]孙作玉,王晖.结构非平稳随机响应方差数值计算方法[J].振动工程学报,2009,22(3):325-328
[1.27] Hoshiya M, Ishii K, Nagata S.Recursive covariance of structural responses [J].Journal of Engineering Mechanics,1984,110(12): 1743-1755
[1.28] To C W S.A stochastic version of the Newmark family of algorithms for discretized dynamic systems [J].Computers and Structures, 1992, 44(33): 667-673
[1.29] To C W S, Liu M L.Recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom non-linear system [J].Computers and Structures, 1993, 48(6): 993-1000
[1.30] Miao B Q.Direct integration variance prediction of random response of nonlinear systems [J].Computers and Structures, 1993, 46(6): 979-983
[1.31]缪炳祺,胡夏夏,许礼深.结构非平稳随机响应分析的Newmark递推算法[J].强度与环境,1996,23(1):34-39
[1.32] Tootkaboni M, Graham-Brady L.Stochastic direct integration schemes for dynamic systems subjected to random excitations [J].Probabilistic Engineering Mechanics, 2010, 25(2): 163-171
[1.33]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
[1.34]朱位秋.非线性随机动力学与控制[M].北京:科学出版社,2003
[1.35] Thomas K, Caughey T.Equivalent linearization techniques [J].Journal of the Acoustical Society of America, 1963, 35(11): 1706-1711
[1.36] Atalik T S, Utku S.Stochastic linearization of mufti-degree-of freedom non-linear systems [J].Earthquake Engineering and Structural Dynamics, 1976, 4(4): 411-420
[1.37] Spanos P D.Stochastic linearization in structural dynamics [J].Applied Mechanics Review, 1981, 34(1): 1-8
[1.38] Zhu W Q.Stochastic averaging methods in random vibration [J].Applied Mechanics Reviews, 1988, 41(5): 189-199
[1.39]陈建兵.随机结构非线性反应概率密度演化分析[D].上海:同济大学,2002
[1.40] Ghanem R G, Spanos P D.Stochastic finite element: a spectral approach [M].New York: Springer-Verlag, 1991
[1.41] Kleiber M, Hien T D.The stochastic finite element method: basic perturbation technique and computer implementation [M].New York: John Wiley & Sons, 1992
[1.42]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[1.43] Giovanni F, Gabriele F.A dynamic stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures [J].Structural Engineering and Mechanics, 2006, 23(6): 599-613
[1.44]车建文.基于可靠性的结构动力优化设计研究[D].西安:西安电子科技大学,1998
[1.45]高伟.随机、智能结构随机振动分析与主动控制研究[D].西安:西安电子科技大学,2003
[1.46]雒卫廷.基于完全概率的随机结构分析与可靠性研究[D].西安:西安电子科技大学,2007
[1.47] Li J, Chen J B.Stochastic dynamics of structures [M].New York: John Wiley & Sons, 2009
[1.48] Shinozuka M.Monte Carlo solution of structural dynamics [J].Computers and Structures, 1972, 2(5): 855-874
[1.49] Shinozuka M, Jan C M.Digital simulation of random processes and its applications [J].Journal of Sound and Vibration, 1972, 25(1): 111-128
[1.50] Shinozuka M, Wen Y K.Monte Carlo solution of nonlinear vibration [J].AIAA Journal, 1972, 10(1): 37-40
[1.51] Astill C J, Noisseir S B, Shinozuka M.Impact loading on structures with random properties [J].Journal of Structural Mechanics, 1972, 1(1): 63-67
[1.52] Sun T C.A finite element method for random differential equations with random coefficients [J].Journal of Numerical Analysis, 1979, 16(6): 1019-1035
[1.53] Jensen H, Iwan W D.Response variability in structural dynamics [J].Earthquake Engineering and Structural Dynamics, 1991, 20(10): 949-959
[1.54] Jensen H, Iwan W D.Response of systems with uncertain parameters to stochastic excitation [J].Journal of Engineering Mechanics, 1992, 118(11): 1012-1025
[1.55] Iwan W D, Jensen H.On the dynamic response of continuous systems including model uncertainty [J].Journal of Applied Mechanics, 1993, 60(2): 484-490
[1.56]李杰.随机结构分析的扩阶系统方法(I)-扩阶系统方程[J].地震工程与工程振动,1995,15(3):111-118
[1.57]李杰.随机结构分析的扩阶系统方法(II)-结构动力分析[J].地震工程与工程振动,1995,15(4):27-35
[1.58]李杰.复合随机振动分析的扩阶系统方法[J].力学学报,1996,28(1):66-75
[1.59] Dostupov B G, Pugachev V S.The equation for the integral of a system of ordinary differential equations containing random parameters [J].Automatika i Telemekhanika, 1957, 18(4): 620-630
[1.60] Ding G Y, Li J.The nonlinear response emulation analysis of stochastic structure subjected to the earthquake excitation [A].New Zealand: The 12th World Earthquake Engineering Conference, 2000
[1.61]丁光莹.钢筋混凝土框架结构非线性反应分析的数值模拟分析[D].上海:同济大学,2001
[1.62] Liu W K, Belytschko T, Mani A.Probabilistic finite elements for nonlinear structural dynamics [J].Computer Methods in Applied Mechanics and Engineering, 1986, 56(1) 61-81
[1.63] Ma A J, Chen S H, Han W Z.Stochastic properties of response for nonlinear structural systems with random parameters [J].Computers and Structures, 1996, 58(6): 1139-1144
[1.64] Klosner J M, Haber S F, Voltz P.Response of non-linear systems with parameter uncertainties [J].International Journal of Non-linear Mechanics, 1992, 27(4): 547-563
[1.65] Bernard P, Wu L M.Stochastic linearization: the theory [J].Journal of Applied Probability 1998, 35(3): 718-730
[1.66] Bernard P.Stochastic linearization: what is available and what is not [J].Computers and Structures, 1998, 67(1): 9-18
[1.67] Zielihski A P, Frey F.On linearization in non-linear structural finite element analysis [J].Computers and Structures, 2001, 79(8): 825-838
[1.68] Anders M, Hori M . Three-dimensional stochastic finite element method for elastic-plastic bodies [J].International Journal for Numerical Methods in Engineering, 2001, 51(4): 449-478
[1.69]钟万勰.一个高效结构随机响应算法系列-虚拟激励法[J].自然科学进展,1996,6(4):394-401
[1.70] Lin J H.Zhao Y, Zhang Y H.Accurate and highly efficient algorithms for structural stationary/non-stationary random responses [J].Computer Methods in Applied Mechanics and Engineering, 2001, 9(1): 103-111
[1.71] Bathe K J.Finite element procedures [M].New Jersey: Prentice-Hall, 1996
[1.72] Yamazaki F, Shinozuka M, Dasgupta G.Neumann expansion for stochastic finite element analysis [J].Journal of Engineering Mechanics, 1988, 114(8): 1335-1345
[1.73]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].成都:西南交通大学,1996
[1.74] Chakraborty S, Dey S S.A stochastic finite element dynamic analysis of structures with uncertain parameters [J].International Journal of Mechanical Sciences, 1998, 40(11): 1071-1087
[1.75]赵雷,陈虬.随机有限元动力分析方法的研究进展[J].力学进展,1999,29(1):9-18
[1.76] Liu W K, Besterfield G, Belytschko T.Transient probabilistic systems [J].Computer Methods in Applied Mechanics and Engineering, 1988, 67(1): 27-54
[1.77]林家浩,夏杰,张亚辉,等.非平稳随机摄动分析中的久期项效应[J].振动工程学报,2003,16(1):124-128
[1.78] Wang F Y, Zhao Y, Lin J H.Stochsatic response analysis of structures with random properties subjected to stationary random excitation[C].Earth and space2010: Engineering, Science, Construction, and Operation in Challenging Environments, 2010, 2949-2957
[1.79]王凤武,楼梦麟.随机参数结构体系的随机地震响应计算方法[J].同济大学学报,2004,32(1):6-9
[1.80] Sniady P, Adamowski R, Kogut G, et al.Spectral stochastic analysis of structures with uncertain parameters [J].Probabilistic Engineering Mechanics, 2008, 23(1): 76-83
[1.81] Ghanem R, Spanos P D.Polynomial chaos in stochastic finite elements [J].Journal of Applied Mechanics, 1990, 57(1): 197-202
[1.82]李杰,魏星.随机结构动力分析的递归聚缩算法[J].固体力学学报,1996,17(3):263-267
[1.83]李杰,廖松涛.线性随机结构在随机激励下动力响应分析[J].力学学报,200,34(3):416-424
[1.84]胡太彬,陈建军,王小兵,等.不均匀随机参数桁架结构的随机反应分析[J].工程力学,2007,24(2):126-131
[1.85]胡太彬,陈建军,徐亚兰.随机参数平面刚架结构频率特性分析的随机因子法[J].机械强度,2006,28(2):196-200
[1.86] Gao W, Chen J J, Ma H B.Dynamic response analysis of closed loop control system for intelligent truss structures based on probability [J].Structural Engineering and Mechanics, 2003, 15(2): 239-248
[1.87]高伟,陈建军.线性随机结构的平稳随机响应分析[J].应用力学学报,2003,20(3):92-95
[1.88] Gao W, Chen J J, Ma J, et al. Dynamic response analysis of stochastic frame structures under nonstationary random excitation [J].AIAA Journal, 2004, 42(9): 1818-1822
[1.89] Gao W, Chen J J, Cui M T, et al.Dynamic response analysis of linear stochastic truss structures under stationary random excitation [J].Journal of Sound and Vibration, 28(2): 311-321
[1.90] Syski R.Stochastic differential equations [M].New York: McGraw-Hill, 1967
[1.91] Fuller A T.Analysis of nonlinear stochastic systems by means of the Fokker-Planck equation [J].International Journal of Control, 1969, 9(6): 603-655
[1.92]李杰,陈建兵.随机动力系统中的广义密度演化方程[J].自然科学进展,2006,16(6):712-719
[1.93] Chen J B, Li J.A note on the principle of preservation of probability and probability density evolution equation [J].Probabilistic Engineering Mechanics, 2009, 24(1): 51-59
[1.94]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[J].北京:地震出版社,1993
[1.95]李桂清,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001
[1.96]陈建兵,李杰.随机机构动力可靠度分析的极值概率密度函数[J].地震工程与工程振动,2004,24(6):39-44
[1.97]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121-125
[1.98]李桂青,曹宏.动力可靠性评述[J].地震工程与工程振动,1983,3(3):42-62
[1.99]欧进萍.国外动力可靠性理论述评[J].武汉建材学院学报,1983,5(2):231-248
[1.100] Coleman J J.Reliability of aircraft structures in resisting chance failure operations [J].Operations Research, 1959, 7(4): 639–645
[1.101] Crandall S H.First crossing probabilities of the linear oscillator [J].Journal of Sound and Vibration, 1970, 12(3): 285-299
[1.102] Yang J N, Shinozuka M.On the first excursion probability in stationary narrow-band random vibration [J].Journal of Applied Mechanics, 1971, 38(4): 1017-1022
[1.103] Yang J N, Shinozuka M.On the first excursion probability in stationary narrow band random vibration-2 [J].Journal of Applied Mechanics, 1972, 39(3): 733-738
[1.104] Yang Y N.Nonstationary envelop process and first excursion probability [J].Journal of Structural Mechanics, 1972, 1(2): 231-248
[1.105] Yang Y N.First excursion probability in nonstationary random vibration [J].Journal of Applied Mechanics, 1973, 26(3): 417-428
[1.106] Madsen H O, Krenk S, Lind N C.Methods of structural safety [M].New Jersey: Prentice-Hall, 1986
[1.107] Roberts J B.An approach to the first-passage problem in random vibration [J].Journal of Sound and Vibration, 1968, 8(2): 301-328
[1.108] Cramer H.On the intersections between the trajectories of a normal stationary stochastic process and a high level [J].Arkiv for Matematik, 1966, 6(2): 337-349
[1.109] Corotis R B, Vanmarcke E H, Cornell C A.First passage of nonstationary random processes[J].Journal of the Engineering Mechanics Division, 1972, 98(2): 401–414
[1.110] Vanmarcke E H.On the distribution of the first-passage time for normal stationary random processes [J].Journal of Applied Mechanics, 1975, 42(2): 215-220
[1.111]李杰,陈建兵.概率密度演化方程-历史、进展与应用[M].上海:同济大学,2008
[1.112] Park B T.Petrosian V.Fokker-Planck equations of stochastic acceleration: a study of numerical method [J].The Astrophysical Journal Supplement Series, 1996, 103(1): 255-267
[2.1] Gasparini D A.Response of MDOF systems to non-stationary random excitation [J].Journal of Engineering Mechanics Division, 1979, 105(1): 13-27
[2.2]王超,徐晖,高耀南,等.非平稳激励下结构动力可靠度计算[J].西安交通大学学报,1993,27(4):47-52
[2.3]肖梅玲,高春涛,叶燎原.结构地震反应在小波基下的动力可靠性分析[J].世界地震工程,2002,18(1):27-33
[2.4] Chaudhuri A, Chakraborty S.Reliability evaluations of 3-D frame subjected to non-stationary earthquake [J].Journal of Sound and Vibration, 2003, 259(4): 797-808
[2.5]石少卿,姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究[J].应用力学学报,1999,16(4):73-77
[2.6]曹晖,赖明,白绍良.基于小波分析的结构动力可靠度估计[J].世界地震工程,2000,16(4):70-77
[2.7] Au S K, Beck J L.First excursion probabilities for linear systems by very efficient importance sampling [J].Probabilistic Engineering Mechanics, 2001, 16(3): 193-207
[2.8] Pradlwarter H J, Schueller G I.Excursion probabilities of non-linear systems [J].International Journal of Non-linear Mechanics, 2004, 39(9): 1447-1452
[2.9] Pradlwarter H J, Schueller G I, Koutsourelakis P S, et al.Application of line sampling simulation method to reliability benchmark problems [J].Structural Safety, 2007,29(3): 208-221
[2.10] Au S K, Beck J L.Estimation of small failure probabilities in high dimensions by subset simulation [J].Probabilistic Engineering Mechanics, 2001, 16(4): 263-277
[2.11] Ching J, Beck J L, Au S K.Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation [J].Probabilistic Engineering
Mechanics, 2005, 20(3): 199-214
[2.12] Au S K, Ching J, Beck J L.Application of subset simulation methods to reliability benchmark problems [J].Structural Safety, 2007, 29(3): 183-193
[2.13] Priestley M B.Evolutionary spectral and non-stationary process [J].Journal of Royal Statistical Society, 1965, 27(2): 204-237.
[2.14] Priestley M B.Power spectral analysis of non-stationary random process [J].Journal of Sound and Vibration, 1967, 6(1): 86-97
[2.15] Priestly M B.Spectral analysis and time series [M].London: Academic Press, 1981
[2.16] Mark W D.Spectral analysis of the convolution and filtering of non-stationary stochastic processes [J].Journal of Sound and Vibration, 1970, 11(1): 19-63
[2.17] Mark W D.Characterization of stochastic transients and transmission media: the method of power-moments spectra [J].Journal of Sound and Vibration, 1972, 22(3): 249-295
[2.18] Loynes R M.On the concept of the spectrum for nonstationary processes [J].Journal of Royal Statistical Society, 1968, 30(1): 1-30
[2.19] Eberly J H, Wodkiewicz K.The time-dependent physical spectrum of light [J].Journal of the Optical Society of America, 1977, 67(9): 1252-1261
[2.20]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
[2.21]李英民,赖明.工程地震动模型化研究综述及展望(Ⅱ)-平稳模型及均匀调制过程[J].重庆建筑大学学报,1998,20(4):111-118
[2.22]李英民,赖明.工程地震动模型化研究综述及展望(Ⅲ)-其它工程学模型与展望[J].重庆建筑大学学报,1998,20(5):108-114
[2.23]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136
[2.24]朱位秋.随机振动[M].北京:科学出版社,1992
[2.25] Rice S O.Mathematical analysis of random noise [J].Bell System Technical Journal,1944, 23(3): 282-332
[2.26] Shinozuka M.Simulation of multivariate and multidimensional random processes [J].Journal of the Acoustical Society of America, 1971, 49(1): 357-368
[2.27] Iannuzzi A, Spinelli P.Artificial wind generation and structural response [J].Journal of Structural Engineering, 1987, 113(12): 2382-2398
[2.28] Saul W E, Jayachandran P, Peyrot A H.Response to stochastic wind of N-degree tall buildings [J].Journal of Structural Engineering, 1976, 102(5): 1059-1075
[2.29] Mignolet M P, Spanos P D.MA to ARMA modeling of wind [J].Journal of Wind Engineering and Industrial Aerodynamics, 1990, 36(1-3): 429-438
[2.30] Mignolet M P, Spanos P D.Optimality in the estimation of a MA system from a long AR model for simulation studies [J].Soil Dynamics and Earthquake Engineering, 1995, 14(6): 445-452
[2.31] Mignolet M P, Spanos P D.A direct determination of ARMA algorithms for the simulation of stationary random processes [J].International Journal of Non-Linear Mechanics, 1990, 25(5): 555-568
[2.32] Saramas E, Shinozuka M.ARMA representation of random processes [J].Journal of Engineering Mechanics, 1985, 111(3): 449-461
[2.33] Shinozuka M, Sato Y.Simulation of nonstationary random process [J].Journal of Engineering Mechanics, 1967, 63(1): 11-40
[2.34] Deodatis G, Shinozuka M.Autoregressive model for non-stationary stochastic process [J].Journal of Engineering Mechanics, 1988, 114(11): 1995-2012
[2.35] Li Y S, Kareem A.Simulation of multivariate nonstationary random process by FFT [J].Journal of Engineering Mechanics, 1991, 117(5): 1037-1058
[2.36] Grigoriu M.Simulation of nonstationary gaussian processes by random trigonometric polynomials [J].Journal of Engineering Mechanics, 1993, 119(2): 328-343
[2.37] Deodatis G.Non-stationary stochastic vector processes: seismic ground motion applications [J].Probabilistic Engineering Mechanics, 1996, 11(3): 149-168
[2.38] Li Y S, Kareem A.Simulation of multivariate nonstationary random processes: Hybrid DFT and digital filtering approach [J].Journal of Engineering Mechanics, 1997,
123(12): 1302-1310
[2.39]杨庆山,姜海鹏,陈英俊.基于相位差谱的时-频非平稳人造地震动的生成[J].地震工程与工程振动,2001,21(3):10-16
[2.40]张建仁,刘扬,许福友,郝海霞.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
[2.41] Cressie N.Statistics for Spatial Data [M].New York: John Wiley & Sons, 1993
[2.42]陈太聪.结构工程自适应控制的参数分析新方法研究及其在大跨度斜拉桥施工中的应用[D].广州:华南理工大学,2003
[2.43]林家浩,钟万勰,张亚辉.大跨度结构抗震计算的随机振动分析方法[J].建筑结构学报,2000,21(1):29-36.
[2.44]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用[M].北京:地震出版社,1993
[2.45]李桂清,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001
[2.46] Nowak A S, Collins K R.Reliability of Structures [M].New York: McGraw-Hill, 2000
[2.47] Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion [J].Bulletin of the Earthquake Research Institute, University of Tokyo, 1957, 35(2): 308-325
[2.48]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21-26
[3.1]李杰.结构动力分析的若干发展趋势[J].世界地震工程,1993,8(2):1-8
[3.2] Shinozuka M.Monte Carlo solution of structural dynamics [J].Computers andStructures, 1972, 2(5): 855-874
[3.3] Shinozuka M, Jan C M.Digital simulation of random processes and its applications [J].Journal of Sound and Vibration, 1972, 25(1): 111-128
[3.4] Shinozuka M, Wen Y K.Monte Carlo solution of nonlinear vibration [J].AIAA Journal, 1972, 10(1): 37-40
[3.5] Astill C J, Noisseir S B, Shinozuka M.Impact loading on structures with random properties [J].Journal of Structural Mechanics, 1972, 1(1): 63-67
[3.6] Ghanem R G, Spanos P D.Stochastic finite element: a spectral approach [M].New York: Springer-Verlag, 1991
[3.7] Kleiber M, Hien T D.The stochastic finite element method: basic perturbation technique and computer implementation [M].New York: John Wiley & Sons, 1992
[3.8]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993
[3.9]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[3.10] Giovanni F, Gabriele F.A dynamic stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures [J].Structural Engineering and Mechanics, 2006, 23(6): 599-613
[3.11]车建文.基于可靠性的结构动力优化设计研究[D].西安:西安电子科技大学,1998
[3.12]高伟.随机、智能结构随机振动分析与主动控制研究[D].西安:西安电子科技大学,2003
[3.13]雒卫廷.基于完全概率的随机结构分析与可靠性研究[D].西安:西安电子科技大学,2007
[3.14] Li J, Chen J B.Stochastic dynamics of structures [M].New York: John Wiley & Sons, 2009
[3.15]曹宏,李秋胜,李芝艳.随机结构动力反应和可靠性分析[J].应用数学和力学,1993,14(10):931-938
[3.16]胡太彬,陈建军,高伟,马娟.平稳随机激励下随机桁架结构动力可靠性分析[J].力学学报,2004,36(2):241-246
[3.17] Spencer B F Jr, Elishakoff I . Reliability of uncertain linear and nonlinear systems[J].Journal of Engineering Mechanics, 1988, 114(1): 135-149
[3.18] Papadimitriou C, Beck J L, Katafydiotis L S.Asymptotic expansions for reliability and moments of uncertain systems [J].Journal of Engineering Mechanics, 1997, 123(12): 1219-1229
[3.19]乔红威,吕震宙.非平稳随机激励下随机结构的动力可靠性分析[J].固体力学学报,2008,29(1):36-40
[3.20]乔红威,吕震宙,关爱锐,刘旭华.平稳随机激励下随机结构动力可靠度分析的多项式逼近法[J].工程力学,2009,26(2):60-64
[3.21] Brenner C E, Bucher C.A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading [J].Probabilistic Engineering Mechanics, 1995, 10(4): 265-273
[3.22]陈颖,王东升,朱长春.随机结构在随机载荷下的动力可靠度分析[J].工程力学,2006,23(10):82-85
[3.23]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121-125
[3.24]陈建兵,李杰.复合随机振动系统的动力可靠度分析[J].工程力学,2005,22(3):52-57
[3.25] Li J, Chen J B, Fan W L.The equivalent extreme-value event and evaluation of the structural system reliability [J].Structural Safety, 2007, 29(1): 112-131
[3.26] Bucher C G, Bourgund U.A fast and efficient response surface approach for structural reliability problems [J].Structural Safety, 1990, 7(1): 57-66
[3.27] Chaudhuri A, Chakraborty S . Reliability of linear structures with parameter uncertainty under non-stationary earthquake [J].Structural Safety, 2006, 28(3): 231-246
[3.28] Zhao Y G, Ono T, Idota H.Response uncertainty and time-variant reliability analysis for hysteretic MDF structures [J].Earthquake Engineering and Structural Dynamics, 1999, 28(10): 1187-1213
[3.29] Zhao Y G, Ono T.New point estimates for probability moments [J].Journal of Engineering Mechanics, 2000, 126(4): 433-436
[3.30]王梓坤.概率论基础及其应用[M].北京:北京师范大学出版社,2007
[3.31]严士健,王隽骧,刘秀芳.概率论基础[M].北京:科学出版社,2009
[4.1] Karhunen K.Uber lineare methoden in der wahrscheinlichkeitsrechnung [M].Annales Academiae Scientiarum Fennicae(Series A1): Mathematica-Physica, 1947
[4.2] Loeve M.Probability theory [M].Berlin: Springer-Verlag, 1977
[4.3] Lumley J L.Stochastic tools in turbulence[M].London: Academic Press, 1970
[4.4]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996
[4.5] Solari G, Carassale L, Tubino F.Proper orthogonal decomposition in wind engineering. Part 1: A state-of-art and some prospects[J].Wind and Structures, 2007, 10(2): 153-176
[4.6] Carassale L, Solari G, Tubino F.Proper orthogonal decomposition in wind engineering. Part 2: Theoretical aspects and some application[J].Wind and Structures, 2007,10(2): 177-208
[4.7] Grigoriu M.Evaluation of Karhunen-Loeve, Spectral, and Sampling Representations for Stochastic Processes [J].Journal of Engineering Mechanics, 2006, 132(2): 179-189
[4.8] Feeny B F, Kappagantu R.On the physical interpretation of proper orthogonal modes in vibrations[J]. Journal of Sound and Vibration, 1998, 211(44): 607-616
[4.9] Ravindra B.Comments on“On the physical interpretation of proper orthogonal modes in vibrations”[J].Journal of Sound and Vibration, 1999, 219(1): 189-192
[4.10] Van Trees H I.Detection, estimation and modulation theory: Part 1 [M]. New York: John Wiley & Sons, 1968
[4.11]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007
[4.12] Phoon K K, Huang S P, Quek S T.Implementation of Karhunen-Loeve expansion for simulation using wavelet-Galerkin scheme[J].Probabilistic Engineering Mechanics, 2002, 17(3): 293-303
[4.13] Phoon K K, Huang H W, Quek S T.Comparison between Karhunen-Loeve and wavelet expansions for simulation of Gaussian processes[J].Computers and Structure,2004, 82(5): 985-991
[4.14] Zhang J, Ellingwood B.Orthogonal series expansions of random fields in reliability analysis[J].Journal of Engineering Mechanics, 1994, 120(12): 2660-2667
[4.15]刘天云,伍朝晖,赵国藩.随机场的投影展开法[J].计算力学学报,1997,14(4):484-489
[4.16]李杰,刘章军.基于标准正交基的随机过程展开法[J].同济大学学报,2006,36(10):1279-1282
[4.17]刘章军,李杰.脉动风速随机过程的正交展开[J].振动工程学报,2008,21(1):96-101
[4.18]李杰,刘章军.随机脉动风场的正交展开法[J].土木工程学报,2008,41(2):49-53
[4.19] Phoon K K, Quek S T, Huang H W.Simulation of non-Gaussian processes using fractile correlation[J].Probabilistic Engineering Mechanics, 2004, 19(4): 287-292
[4.20] Phoon K K, Huang H W, Quek S T.Simulation of strongly non-Gsussian processes using Karhunen-Loeve expansion [J].Probablisitic Engineering Mechanics, 2005, 20(2): 188-198
[4.21] Li L B, Phoon K K, Quek S T.Comparison between Karhunen-Loeve expansion and translation-based simulation of non-Gaussian processes [J]. Computers and Structures, 2007, 85(5-6): 264-276
[4.22]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
[5.1]李国豪.工程结构抗震动力学[M].上海:科学技术出版社,1980
[5.2] Housner G W.Characteristic of strong motion earthquakes [J].Bulletin of the Seismological Society of America, 1947, 37(1): 17-31
[5.3] Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion [J].Bulletin of the Earthquake Research Institute, University of Tokyo, 1957, 35(2):308-325
[5.4]胡聿贤,周锡元.弹性体系在平稳和平稳化地面运动下的反应[M].中国科学院土木建筑研究所地震工程研究报告集(第1集).北京:科学出版社,1962:33-50
[5.5] Clough R W, Penzien J.Dynamics of structures [M].New York: McGraw-Hill, 1993
[5.6]欧进萍,牛荻涛.地震地面运动随机模型的参数及其结构效应[J].哈尔滨建筑工程学院学报,1990,10(2):70-76
[5.7]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5
[5.8]李英明,刘立平,赖明.工程地震动随机功率谱模型的分析与改进[J].2008,25(3):43-48
[5.9]范立础,胡世德,叶爱君.大跨度桥梁抗震设计[M].北京:人民交通出版社,2001
[5.10]陈海斌.大跨度桥梁非线性抗震分析[D].广州:华南理工大学,2006
[5.11]徐升桥,任为东,彭岚平,等.广州市新光快速路工程新光大桥施工图设计[Z].北京:铁道部专业设计院,2004
[5.12]谭林.基于动力指纹的结构损伤识别可靠度方法研究[D].广州:华南理工大学,2010
[5.13] Amin M, Ang A H S.Nonstationary stochastic model of earthquake motion [J].Engineering Mechanics Division, 1968, 94(2): 559-584
[5.14]李英民,赖明.工程地震动模型化研究综述及展望(II)-平稳模型及均匀调制过程[J].重庆建筑大学学报,1998,20(4):111-118
[5.15]广东省地震工程勘测中心.广州新光快速路工程场地地震安全性评价报告.2003
[5.16]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10
[5.17]田利,李宏男.基于《电力设施抗震设计规范》的地震动随机模型参数研究[J].防灾减灾工程学报,2010,30(1):17-22
[5.18]李跃,张健峰,卢汝生,等.广州新光大桥[M].北京:人民交通出版社,2009
[5.19]朱伯龙,董振祥.钢筋混凝土非线性分析[M].上海:同济大学出版社,1985
[5.20] Mander J B, Priestley M J N,Park R.Theoretical stress-strain model for confined concrete [J].Journal of Structural Engineering, 1988, 114(8): 1804-1826