结构非线性风振的路径积分方法
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摘要
通过引入相关脉动风速滤波,将结构非线性风振方程转变为Ito随机微分方程的形式;该方程的解过程具有Markov性质.在时域内将状态方程展开,利用其瞬时线性化随机方程的解析解,基于路径积分给出了结构非线性风振响应概率密度的形式解,得到了一种分析结构非线性风振响应的新方法.对桅杆算例的数值分析表明,该方法较线性频域分析方法和非线性时域积分方法具有更好的准确性和有效性.
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated.With the white noise filter of turbulent-wind fluctuations,the nonlinear motion equation of structures subjected to wind load was modeled as the Ito's stochastic differential equation.The state vector associated with such a model is a diffusion process.A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations,the formal probabilistic density of the structure response was developed by the path integral technique.It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis,the proposed approach is highlighted by high accuracy and robustness.The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated.With the white noise filter of turbulent-wind fluctuations,the nonlinear motion equation of structures subjected to wind load was modeled as the Ito's stochastic differential equation.The state vector associated with such a model is a diffusion process.A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations,the formal probabilistic density of the structure response was developed by the path integral technique.It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis,the proposed approach is highlighted by high accuracy and robustness.The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
引文
[1]王肇民,王之宏,颜明忠.桅杆结构[M].北京:科学出版社,2000.
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[3]Kahla N Ben.Dynamic analysis of guyed towers[J].Engng Struct,1994,16(4):293—301.
[4]王肇民,程凌勇.桅杆结构动力特性研究[J].建筑结构学报,1993,14(5):2—10.
[5]马星,李泽,蒋涛.考虑纤绳振动桅杆结构的随机风振分析[J].同济大学学报,1998,26(6):631—635.
[6]Yim S C S,Lin H.Unified analysis of complex nonlinear motions via densities[A].In:Naess A,KrenkS Eds.Proceedings of the IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics[C].Dordrecht:Kluwer Academic Publishers,1996,489—501.
[7]Naess A.Chaos and nonlinear stochastic dynamics[J].Probabilistic Eng Mechanics,2000,15(1):37—47.
[8]马星,邓洪洲.桅杆结构随机风振的离散分析法[J].工程力学,2002,19(1):34—37.
[9]MA Xing,WANG Zhong_gang,DENG Hong_zhou.Theoretical and experimental research on dynamicbehavior of guyed masts under wind load[J].Acta Mechanical Solida Sinica,2004,17(2):166—171.
[10]Paola M Di,Ricciardi G,Vasta M.A method for the probabilistic analysis of nonlinear system[J].Probabilistic Eng Mechanics,1995,10(3):1—10.
[11]Peil U,Noelle H.Guyed masts under wind load[J].J Wind Eng and Industr Aerodyn,1992,44:2129—2140.
[12]张炳根,赵玉芝.科学和工程中的随机微分方程[M].北京:海洋出版社,1980.
[13]王仲刚,邓洪洲.桅杆风振试验研究[J].工程力学,2003,20(5):42—47.
[14]Liu S C.Solutions of Fokker_Planck equation with applications in nonlinear random vibration[J].TheBell System Technical Journal,1969,48:2031—2051.
[15]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1995.
[2]Peil U,N lle H.On fatigue of guyed masts due to wind load[A].In:Schu ller G I,YAO Fen Eds.Structural Safety&Reliability[C].Rotterdam:Balkema,1994,1132—1140.
[3]Kahla N Ben.Dynamic analysis of guyed towers[J].Engng Struct,1994,16(4):293—301.
[4]王肇民,程凌勇.桅杆结构动力特性研究[J].建筑结构学报,1993,14(5):2—10.
[5]马星,李泽,蒋涛.考虑纤绳振动桅杆结构的随机风振分析[J].同济大学学报,1998,26(6):631—635.
[6]Yim S C S,Lin H.Unified analysis of complex nonlinear motions via densities[A].In:Naess A,KrenkS Eds.Proceedings of the IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics[C].Dordrecht:Kluwer Academic Publishers,1996,489—501.
[7]Naess A.Chaos and nonlinear stochastic dynamics[J].Probabilistic Eng Mechanics,2000,15(1):37—47.
[8]马星,邓洪洲.桅杆结构随机风振的离散分析法[J].工程力学,2002,19(1):34—37.
[9]MA Xing,WANG Zhong_gang,DENG Hong_zhou.Theoretical and experimental research on dynamicbehavior of guyed masts under wind load[J].Acta Mechanical Solida Sinica,2004,17(2):166—171.
[10]Paola M Di,Ricciardi G,Vasta M.A method for the probabilistic analysis of nonlinear system[J].Probabilistic Eng Mechanics,1995,10(3):1—10.
[11]Peil U,Noelle H.Guyed masts under wind load[J].J Wind Eng and Industr Aerodyn,1992,44:2129—2140.
[12]张炳根,赵玉芝.科学和工程中的随机微分方程[M].北京:海洋出版社,1980.
[13]王仲刚,邓洪洲.桅杆风振试验研究[J].工程力学,2003,20(5):42—47.
[14]Liu S C.Solutions of Fokker_Planck equation with applications in nonlinear random vibration[J].TheBell System Technical Journal,1969,48:2031—2051.
[15]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1995.
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