K-L分解在非平稳地震响应分析中的应用(英文)
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摘要
介绍了一种非平稳地震激励下结构随机响应的分析方法。按照K-L分解理论,地震激励可以描述为一系列确定性函数与随机系数乘积的线性组合形式。对于线性结构,地震激励的每项K-L展开级数对应于一项结构响应。因此,任何确定性动力时程积分方法可以应用于求解与KL展开级数相对应的结构响应。这为商用有限元软件用于随机地震响应分析打开了方便之门,同时也有利于提高随机振动分析在实际工程中的应用。一个受均匀调制非平稳地震激励下的21层框架结构用于阐明这种方法。
The objective of the present work is introduced to a new procedure for random response analysis of structure subjected to non-stationary seismic excitation.According to Karhunen-Loeve(K-L)expansion theorem,which allows to represent random seismic random excitation as a series terms involving a complete set of deterministic functions with corresponding random coefficients.Clearly,for linear structures,each deterministic term of K-L expansion of the seismic excitation corresponds to a response.Therefore,any available deterministic dynamic integration scheme can be applied to calculate structural response associated with each term of K-L expansion of excitation process.This in turn opens the avenue for the use of commercial deterministic finite element packages in seismic random analysis,which may greatly enhance the acceptance and use of random analysis in engineering practices.A 21-story frame structure subjected to uniformly modulated non-stationary seismic excitation was used to demonstrate the procedure.
The objective of the present work is introduced to a new procedure for random response analysis of structure subjected to non-stationary seismic excitation.According to Karhunen-Loeve(K-L)expansion theorem,which allows to represent random seismic random excitation as a series terms involving a complete set of deterministic functions with corresponding random coefficients.Clearly,for linear structures,each deterministic term of K-L expansion of the seismic excitation corresponds to a response.Therefore,any available deterministic dynamic integration scheme can be applied to calculate structural response associated with each term of K-L expansion of excitation process.This in turn opens the avenue for the use of commercial deterministic finite element packages in seismic random analysis,which may greatly enhance the acceptance and use of random analysis in engineering practices.A 21-story frame structure subjected to uniformly modulated non-stationary seismic excitation was used to demonstrate the procedure.
引文
1Zhu W Q.Random vibration keferences.Beijing:Science Press,1992
2Soong TT,Grigoriu M.Random vibration of mechanical and structur-al systems.New Jersey:Prentice-Hall,1993
3Lin J H,Zhang Y H.Pseudo-excitation method of random vibration.Beijing:Science Press,2004
4Lin J H,Zhong W X,Zhang W S.Precise integration of the variance matrix of structural non stationary random responses.Journal of Vibra-tion Engineering,1999;12(1):1—8
5Sun Z Y,Wang H.Calculation method of the variance matrix of struc-tural non-stationary random responses.Journal of Vibration Engineer-ing,2009;22(3):325—328
6Hoshiya M,Ishii K,Nagata S.Recursive covariance of structural re-sponses.Journal of Engineering Mechanics,1984;110(12):1743—1755
7To C W S.A stochastic version of the Newmark family of algorithms for discretized dynamic systems.Computers and Structures,1992;44(33):667—673
8To C W S,Liu ML.Recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom non-linear system.Computers and Structures,1993,48(6):993—1000
9Miao B Q.Direct integration variance prediction of random response of nonlinear systems.Computers and Structures,1993;46(6):979—983
10Miao B Q,Hu X X,Xu L S.Recursive Newmark algorithm for the analysis of nonstationary random structural response.Structure and Environment Engineering,1996;23(1):34—39
11Newmark N M.A method of computation for structural dynamics.Journal of Engineering Mechanics,1959;85(3):67
12Wilson E L.A computer program for dynamic stress analysis of un-derground structures.SESMReport(No68—1),University of Cal-ifornia,1968
13Karhunen K.Uber lineare methoden in der wahrscheinlichkeitsrech-nung.Annales Academiae ScientiarumFennicae(Series A1):Math-ematica-Physica,1947
14Loeve M.Probability theory.Berlin:Springer-Verlag,1977
15Ghanem R,Spanos P D.Stochastic finite element:a spectral ap-proach.New York:Springer,1991
16Phoon K K,Huang S P,Quek S T.Implementation of Karhunen-Loeve expansion for simulation using wavelet-Galerkin scheme.Probabilistic Engineering Mechanics,2002,17(3):293—303
17Phoon KK,Huang HW,Quek S T.Comparison between Karhunen-Loeve and wavelet expansions for simulation of Gaussian proces-ses.Computers and Structure,2004;82(5):985—991
18Zhang J,Ellingwood B.Orthogonal series expansions of random fields in reliability analysis.Journal of Engineering Mechanics,1994;120(12):2660—2667
19Liu TY,Wu Z H,Zhao G F.Projective expansion method of ran-dom fields.Chinese Journal of Computational Mechanics,1997,14(4):484—489
20Li J,Liu Z J.Expansion method of stochastic processes based on normalized orthogonal bases.Journal of Tongji University,2006;36(10):1279—1282
21Schueller G I,Pradlwater HJ.Uncertainty analysis of complexstruc-tural systems.International Journal for Numerical Methods in Engi-neering,80(6—7):881—913
22Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion.Bulletin of the Earthquake Research Institute,Uni-versity of Tokyo,1957;35(2):308—325
23Clough R W,Penzien J.Dynamics of structures.NewYork:McGraw-Hill,1993
24Chen X F,Xu R.Common models of earthquake ground motion and calculation of their correlation functions.Supervision Test and Cost of Construction,2009;2(6):15—18
2Soong TT,Grigoriu M.Random vibration of mechanical and structur-al systems.New Jersey:Prentice-Hall,1993
3Lin J H,Zhang Y H.Pseudo-excitation method of random vibration.Beijing:Science Press,2004
4Lin J H,Zhong W X,Zhang W S.Precise integration of the variance matrix of structural non stationary random responses.Journal of Vibra-tion Engineering,1999;12(1):1—8
5Sun Z Y,Wang H.Calculation method of the variance matrix of struc-tural non-stationary random responses.Journal of Vibration Engineer-ing,2009;22(3):325—328
6Hoshiya M,Ishii K,Nagata S.Recursive covariance of structural re-sponses.Journal of Engineering Mechanics,1984;110(12):1743—1755
7To C W S.A stochastic version of the Newmark family of algorithms for discretized dynamic systems.Computers and Structures,1992;44(33):667—673
8To C W S,Liu ML.Recursive expressions for time dependent means and mean square responses of a multi-degree-of-freedom non-linear system.Computers and Structures,1993,48(6):993—1000
9Miao B Q.Direct integration variance prediction of random response of nonlinear systems.Computers and Structures,1993;46(6):979—983
10Miao B Q,Hu X X,Xu L S.Recursive Newmark algorithm for the analysis of nonstationary random structural response.Structure and Environment Engineering,1996;23(1):34—39
11Newmark N M.A method of computation for structural dynamics.Journal of Engineering Mechanics,1959;85(3):67
12Wilson E L.A computer program for dynamic stress analysis of un-derground structures.SESMReport(No68—1),University of Cal-ifornia,1968
13Karhunen K.Uber lineare methoden in der wahrscheinlichkeitsrech-nung.Annales Academiae ScientiarumFennicae(Series A1):Math-ematica-Physica,1947
14Loeve M.Probability theory.Berlin:Springer-Verlag,1977
15Ghanem R,Spanos P D.Stochastic finite element:a spectral ap-proach.New York:Springer,1991
16Phoon K K,Huang S P,Quek S T.Implementation of Karhunen-Loeve expansion for simulation using wavelet-Galerkin scheme.Probabilistic Engineering Mechanics,2002,17(3):293—303
17Phoon KK,Huang HW,Quek S T.Comparison between Karhunen-Loeve and wavelet expansions for simulation of Gaussian proces-ses.Computers and Structure,2004;82(5):985—991
18Zhang J,Ellingwood B.Orthogonal series expansions of random fields in reliability analysis.Journal of Engineering Mechanics,1994;120(12):2660—2667
19Liu TY,Wu Z H,Zhao G F.Projective expansion method of ran-dom fields.Chinese Journal of Computational Mechanics,1997,14(4):484—489
20Li J,Liu Z J.Expansion method of stochastic processes based on normalized orthogonal bases.Journal of Tongji University,2006;36(10):1279—1282
21Schueller G I,Pradlwater HJ.Uncertainty analysis of complexstruc-tural systems.International Journal for Numerical Methods in Engi-neering,80(6—7):881—913
22Kanai K.Semi-empirical formula for the seismic characteristics of the ground motion.Bulletin of the Earthquake Research Institute,Uni-versity of Tokyo,1957;35(2):308—325
23Clough R W,Penzien J.Dynamics of structures.NewYork:McGraw-Hill,1993
24Chen X F,Xu R.Common models of earthquake ground motion and calculation of their correlation functions.Supervision Test and Cost of Construction,2009;2(6):15—18
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