Nonlinear response of structures subjected to stochastic excitations via probability density evolution method

Advances in Structural Engineering

Volumn 17, Issue 6, 2014, Pages 801-816

  Peng, Yongbo ^a,b   Chen, Jianbing ^a,b   Li, Jie ^a,b  

^a Tongji University   (China)

^b TONGJI UNIVERSITY   (China)

Author keywords

Monte Carlo simulation; nonlinear systems; probability density evolution method; pseudo excitation method; Sobol' sequences; stochastic harmonic function

Indexed keywords

DYNAMIC LOADS; DYNAMIC RESPONSE; HARMONIC FUNCTIONS; MONTE CARLO METHODS; NONLINEAR SYSTEMS; POWER SPECTRAL DENSITY; RANDOM PROCESSES; RELIABILITY ANALYSIS; STOCHASTIC MODELS; STRUCTURES (BUILT OBJECTS); WHITE NOISE;

GENERALIZED DENSITY EVOLUTION EQUATION; PERFORMANCE AND RELIABILITIES; PROBABILITY DENSITY EVOLUTION METHOD; PROBABILITY DENSITY EVOLUTION METHODS (PDEM); PSEUDO EXCITATION METHODS; SOBOL' SEQUENCES; SPECIFIED POWER SPECTRAL DENSITY; STOCHASTIC DYNAMIC RESPONSE;

STOCHASTIC SYSTEMS;

EID: 84903513605     PISSN: 13694332     EISSN: None     Source Type: Journal    
DOI: 10.1260/1369-4332.17.6.801     Document Type: Article

References (41)

1. Belytschko, T., Liu, W.K. and Moran, B. (2000). Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, New York, USA.
2. Caughey, T.K. and Ma, F. (1982). "The exact steady-state solution of a class of non-linear stochastic systems " , International Journal of Non-Linear Mechanics, Vol. 17, No. 3, pp. 137-142.
3. Chen, J.B. and Li, J. (2013). " Optimal determination of frequencies in the spectral representation of stochastic processes" , Computational Mechanics, Vol. 51, pp. 791-806.
4. Chen, J.B. and Zhang, S.H. (2013). "Improving point selection in cubature by a new discrepancy " , SIAM Journal on Scientific Computing, Vol. 35, No. 5, pp. A2121-A2149.
5. Chen, J.B., Ghanem, R. and Li, J. (2009). "Partition of the probability space in probability density evolution analysis of nonlinear stochastic structures" , Probabilistic Engineering Mechanics, Vol. 24, No. 1, pp. 27-42.
6. Chen, J.B., Peng, Y.B. and Li, J. (2011). "A note on the pseudoexcitation method ", Chinese Journal of Computational Mechanics, Vol. 28, No. 2, pp. 163-167. (in Chinese)
7. Chen, J.B., Sun, W.L., Li, J. and Xu, J. (2013). " Stochastic harmonic function representation of stochastic processes ", Journal of Applied Mechanics, Vol. 80, No. 1, pp. 011001-1-11.
8. Chung, J. and Lee, J.M. (1994). " A new family of explicit time integration methods for linear and nonlinear structural dynamics" , International Journal for Numerical Methods in Engineering, Vol. 37, pp. 3961-3976.
9. Clough, R.W. and Penzien, J. (1993). Dynamics of Structures (2nd Edition), McGraw-Hill: New York, USA.
10. Cui, L.J., Lu, Z.Z. and Wang, Q. (2012). " Parametric sensitivity analysis of the importance measure" , Mechanical Systems and Signal Processing, Vol. 28, pp. 482-491.
11. Dick, J. and Pillichshammer, F. (20 10). Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press.
12. Fang, T. (1995). Engineering Random Vibration. National Defense Industry Press, Beijing, China. (in Chinese
13. Gitterman, M. (2005). The Noisy Oscillator: the First Hundred Years, from Einstein until Now. World Scientific, Singapore.
14. Goller, B., Pradlwarter, H.J. and Schuë ller, G.I. (2013). "Reliability assessment in structural dynamics" , Journal of Sound and Vibration, Vol. 332, pp. 2488-2499.
15. Landau, L.D. and Lifshitz, E.M. (2007). Quantum Mechanics (Nonrelativistic theory) (Third Edition). Elsevier (Singapore) Pte Ltd.
16. Li, J. (1996). Stochastic Structural Systems: Analysis and Modelling, Science Press, Beijing, China.
17. Li, J. and Chen, J.B. (2005). "Dynamic response and reliability analysis of structures with uncertain parameters " , International Journal for Numerical Methods in Engineering, Vol. 62, pp. 289-315. (Pubitemid 40047394)
18. Li, J. and Chen, J.B. (2008). "The principle of preservation of probability and the generalized density evolution equation" , Structural Safety, Vol. 30, pp. 65-77. (Pubitemid 47371934)
19. Li, J. and Chen, J.B. (2009). Stochastic Dynamics of Structures. John Wiley & Sons, Singapore.
20. Li, J. and Ren, X.D. (2010). "Homogenization-based multi-scale damage theory " , Science China: Physics, Mechanics & Astronomy, Vol. 53, No. 4, pp. 690-698.
21. Li J.Chen J.B.Sun W.L.Peng, Y.B. (2012a) Advances of probability density evolution method for nonlinear stochastic systems, Probabilistic Engineering Mechanics.28, 132-142.
22. Li, J., Yan, Q. and Chen, J.B. (2012b). " Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures" , Probabilistic Engineering Mechanics, Vol. 27, No. 1, pp. 19-28.
23. Lin, Y.K. (1967). Probab ilistic Theory of Structural Dynamics, McGraw-Hill, New York, USA.
24. Science Press Beijing, China. in Chinese
25. Lin, J.H. and Zhang, Y.H. (2004). Pseudo-Excitation Method for Analysis of Random Vibration, Science Press, Beijing, China. (in Chinese) Lutes, L.D. and Sarkani, S. (2004). Random Vibrations: Analysis of Structural and Mechanical Systems, Elsevier, Amsterdam, Netherland.
26. Loè ve, M. (1977). Probability Theory, Springer-Verlag, Berlin, Germany.
27. Ma, F., Zhang, H., Bockstedte, A., Foliente, G.C. and Paevere, P. (2004). " Parameter analysis of the differential model of hysteresis" , Journal of Applied Mechanics, Vol. 71, pp. 342-349. (Pubitemid 40122603)
28. Moshinsky, M. and Smirnov, Y.F. (1996). The Harmonic Oscillator in Modern Physics, Harwood Academic Publishers, Amsterdam, Netherland.
29. Pais, A. (1982). Subtle is the Lord-the Science and the Life of Albert Einstein, Oxford University Press, New York, USA.
30. Peng, Y.B., Chen, J.B. and Li, J. (2010). " Comparative study between generalized density evolution equation and cla ssical random vibration analysis" , Chinese Quarterly of Mechanics, Vol. 31, No. 2, pp. 151-158. (in Chinese
31. Schuë ller, G.I. (1997). " A state-of-the-art report on computational stochastic mechanics" , Probabilistic Engineering Mechanics, Vol. 12, No. 4, pp. 197-321. (Pubitemid 127668995)
32. Shinozuka, M. and Deodatis, G. (1991). "Simulation of stochastic processes by spectral representation " , Applied Mechanics Review, Vol. 44, No. 4, pp. 191-204.
33. Soong, T.T. (1973). Random Differential Equations in Science and Engineering, Academic Press, New York, USA.
34. Spanos, P.D., Beer , M. and Red-Horse, J. (2007). " Karhunen-Loéve expansion of stochastic processes with a modified exponential covariance kernel" , Journal of Engineering Mechanics, Vol. 133, No. 7, pp. 773-779. (Pubitemid 46995164)
35. Vanmarcke, E . (1997). Quantum Origins of Cosmic Structure, A.A. Balkema Publishers, Brookfield, USA.
36. Vanmarcke, E. (2010). Random Fields: Analysis and Synthesis (Revised and Expanded New Edition), World Scientific, Hackensack, USA.
37. Wang, D. and Li, J. (2011). "Physical random function model of ground motions for engineering purposes " , Science China: Technological Sciences, Vol. 54, No. 1, pp. 175-182.
38. Wang, D. and Li, J. (2012). " A random physical model of seismic ground motion field on local engineering site" , Science China: Technological Sciences, Vol. 55, No. 7, pp. 2057-2065.
39. Yan, Q., Peng, Y.B. and Li, J. (2013). " Scheme and application of phase delay spectrum towards spatial stochastic wind fields" , Wind & Structures, Vol. 16, No. 5, pp. 433-455.
40. Zhu, W.Q. (1992). Random Vibration, Science Press, Beijing, China. (in Chinese
41. Zhu, W.Q. (2006). " Nonlinear stochastic dynamics and control in Hamiltonian formulation" , Applied Mechanics Reviews, Vol. 59, pp. 230-248.