复合随机振动系统的动力可靠度分析
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摘要
建议了一类新的复合随机振动系统动力可靠度分析方法。基于复合随机振动系统反应分析的密度演化方法,根据首次超越破坏准则,对密度演化方程施加相应的边界条件,进而求解密度演化方程,在安全域内积分给出结构的动力可靠度。结合精细时程积分方法与具有TVD性质的差分格式,研究了基于密度演化方法求解结构动力可靠度问题的数值方法。以受到随机地震作用、具有随机参数的八层层间剪切型结构为例,进行了结构动力可靠度分析并与随机模拟结果进行了比较。研究表明,建议的方法具有较高的精度和效率。
A new dynamic reliability assessment method for double random vibration systems is proposed, in which the randomness involved in the structural parameters and excitation is taken into account. Through the probability density evolution method, the instantaneous probability density function of response of double random vibration systems is numerically obtained. Based on this method, an absorbing boundary condition, according to the first passage criterion, is imposed on the governing probability density evolution equation. The integration of the probability density function, which is obtained from the initial-boundary-value partial differential equation over the safe domain, will then give the dynamic reliability. A numerical algorithm is studied by combining the precise time integration and the finite difference method with TVD schemes. An 8-story frame with random parameters under random earthquake excitation is investigated to assess the dynamic reliability. The results are compared with those obtained by the Monte Carlo simulation. It is shown that the proposed method is of high accuracy and efficiency.
A new dynamic reliability assessment method for double random vibration systems is proposed, in which the randomness involved in the structural parameters and excitation is taken into account. Through the probability density evolution method, the instantaneous probability density function of response of double random vibration systems is numerically obtained. Based on this method, an absorbing boundary condition, according to the first passage criterion, is imposed on the governing probability density evolution equation. The integration of the probability density function, which is obtained from the initial-boundary-value partial differential equation over the safe domain, will then give the dynamic reliability. A numerical algorithm is studied by combining the precise time integration and the finite difference method with TVD schemes. An 8-story frame with random parameters under random earthquake excitation is investigated to assess the dynamic reliability. The results are compared with those obtained by the Monte Carlo simulation. It is shown that the proposed method is of high accuracy and efficiency.
引文
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[12]陈建兵,李杰.随机结构复合随机振动分析的概率密度演化方法[J].工程力学,2004,21(3):90-95.Chen Jianbing,Li Jie.The probability density evolution method for compound random vibration of stochastic structures[J].Engineering Mechanics,2004,21(3):90-95.(in Chinese)
[13]Loeve M.Probability theory[M].Berlin:Springer-Verlag,1977.
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[15]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.Zhong Wanxie.The precise integration for structural dynamic equations[J].Journal of Dalian University of Technology,1994,34(2):131-136.(in Chinese)
[16]Lin J H,Shen W P,Williams F W.Accurate high-speed computation of nonstationary random seismic response[J].Engineering Structures,1997.19(7):586-593.
[17]Shen M Y,Zhang Z B,Niu X L.Some advances in study of high order accuracy and high resolution finite difference schemes[A].Dubois F,Wu H M ed.New advances in computational fluid dynamics[C].Beijing:Higher Education Press,2001.
[18]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.Liu Ruxun,Shu Qiwang.Some new methods in computational fluid dynamics[M].Beijing:Science Press,2003.(in Chinese)
[2]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.Li Jie.The expanded system method for double random vibration analysis[J].Acta Mechanica Sinica,1996,28(1):66-75.(in Chinese)
[3]Li J,Liao S T.Response analysis of stochastic parameter structures under non stationary random excitation[J].Computational Mechanics,2001,27(1):61-68.
[4]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):931-937.Cao Hong,Li Qiusheng,Li Zhiyan.Dynamic response and reliability analysis of stochastic structures[J].Applied Mathematics and Mechanics,1993,14(10):931-937.(in Chinese)
[5]Spencer B F Jr.,Elishakoff I.Reliability of uncertain linear and nonlinear systems[J].Journal of Engineering Mechanics,1988,114(1):135-149.
[6]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.
[7]Igusa T,Der Kiureghian A.Response of uncertain systems to stochastic excitation[J].Journal of Engineering Mechanics,1988,114(5):812-833.
[8]Brenner C E,Bucher C.A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading[J].Probabilistic Engineering Mechanics,1995,10:265-273.
[9]张义民,刘巧伶,闻邦椿.非线性随机系统的独立失效模式可靠度灵敏度[J].力学学报,2003,35(1):117-120.Zhang Yimin,Liu Qiaoling,Wen Bangchun.Sensitivity of reliability in nonlinear random systems with independent failure modes[J].Acta Mechanica Sinica,2003,35(1):117-120.(in Chinese)
[10]Li J,Chen J B.Probability density evolution method for dynamic response analysis of stochastic structures[A].Zhu W Q,Cai G Q,Zhang R C ed.Advances in Stochastic Structural Dynamics,Proceedings of the Fifth International Conference on Stochastic Structural Dynamics[C].Boca Raton:CRC Press,2003.309-316.
[11]李杰,陈建兵.随机结构动力反应分析的概率密度演化方法[J].力学学报,2003,35(4):437-442.Li Jie,Chen Jianbing.The probability density evolution method for dynamic response analysis of stochastic structures[J].Acta Mechanica Sinica,2003,35(4):437-442.(in Chinese)
[12]陈建兵,李杰.随机结构复合随机振动分析的概率密度演化方法[J].工程力学,2004,21(3):90-95.Chen Jianbing,Li Jie.The probability density evolution method for compound random vibration of stochastic structures[J].Engineering Mechanics,2004,21(3):90-95.(in Chinese)
[13]Loeve M.Probability theory[M].Berlin:Springer-Verlag,1977.
[14]Syski R.Stochastic differential equations[A].In:Saaty T L(ed).Modern Nonlinear Equations[M].McGraw-Hill:New York,1967.
[15]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.Zhong Wanxie.The precise integration for structural dynamic equations[J].Journal of Dalian University of Technology,1994,34(2):131-136.(in Chinese)
[16]Lin J H,Shen W P,Williams F W.Accurate high-speed computation of nonstationary random seismic response[J].Engineering Structures,1997.19(7):586-593.
[17]Shen M Y,Zhang Z B,Niu X L.Some advances in study of high order accuracy and high resolution finite difference schemes[A].Dubois F,Wu H M ed.New advances in computational fluid dynamics[C].Beijing:Higher Education Press,2001.
[18]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.Liu Ruxun,Shu Qiwang.Some new methods in computational fluid dynamics[M].Beijing:Science Press,2003.(in Chinese)
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