Direct derivation of response moment and cumulant equations for non-linear stochastic problems

International Journal of Non-Linear Mechanics

Volumn 35, Issue 5, 2000, Pages 817-835

  Lutes, Loren D ^a   Papadimitriou, Costas ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF THESSALY   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICS; EQUATIONS OF MOTION; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

CUMULANT EQUATIONS; FOKKER-PLANCK EQUATION; NON GAUSSIAN DELTA CORRELATED PROCESSES; NONLINEAR STOCHASTIC PROBLEMS; RESPONSE MOMENT;

NONLINEAR SYSTEMS;

EID: 0034276242     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(99)00061-X     Document Type: Article

References (29)

1. L.D. Lutes, S. Sarkani, Stochastic Analysis of Structural and Mechanical Vibrations, Prentice-Hall, Englewood Cliffs, NJ, 1997.
2. Y.K. Lin, Probabilistic Theory of Structural Dynamics, McGraw-Hill Book Company, New York, 1967. Reprinted in 1976 by Krieger Publishing Co., Melbourne, FL.
3. Spanos P.-T.D. Spectral moments calculation of linear system output. J. Appl. Mech. ASME. 50:1983;901-903.
4. Di Paola M., Muscolino G. Differential moment equations of FE modeled structures with geometrical non-linearities. Int. J. Non-Linear Mech. 25:1990;363-373.
5. Di Paola M., Falsone G., Pirotta A. Stochastic response analysis of nonlinear systems under Gaussian inputs. Probab. Eng. Mech. 7:1992;15-21.
6. Lutes L.D., Chen D.C.-K. Stochastic response moments for linear systems. Probab. Eng. Mech. 7(3):1992;165-173.
7. Hu S.-L.J. Responses of dynamic systems excited by non-Gaussian pulse processes. J. Eng. Mech. ASCE. 119(9):1993;1818-1827.
8. Di Paola M., Falsone G. Stochastic dynamics of MDOF structural systems under non-normal filtered inputs. Probab. Eng. Mech. 9(4):1994;265-272.
9. Falsone G. Cumulants and correlations for nonlinear systems under non-stationary delta-correlated processes. Probab. Eng. Mech. 9(3):1994;157-165.
10. Papadimitriou C., Lutes L.D. Approximate analysis of higher cumulants for MDF random vibration. Probab. Eng. Mech. 9(1):1994;71-82.
11. Hu S.-L.J. Parametric random vibrations under non-Gaussian pulse processes. J. Eng. Mech. ASCE. 121(12):1995;1366-1371.
12. Papadimitriou C., Lutes L.D. Stochastic cumulant analysis of MDOF systems with polynomial-type nonlinearities. Probab. Eng. Mech. 11(1):1996;1-13.
13. Wojtkiewicz S.F., Spencer B.F., Bergman L.A. On the cumulant-neglect closure method in stochastic dynamics. Int. J. Non-Linear Mech. 31(5):1996;657-684.
14. Di Paola M., Falsone G. Higher order statistics of the response of MDOF linear systems excited by linearly parametric white noises and external excitations. Probab. Eng. Mech. 12(3):1997;179-188.
15. Di Paola M., Falsone G. Higher order statistics of the response of MDOF systems under polynomials of filtered normal white noises. Probab. Eng. Mech. 12(3):1997;189-196.
16. Hasofer A.M., Grigoriu M. A new perspective on the moment closure method. J. Appl. Mech. 62(2):1995;527-532.
17. Hu S.-L.J. Response cumulant equations for dynamic systems under delta-correlated processes. J. Eng. Mech. ASCE. 123(2):1997;174-177.
18. Grigoriu M., Waisman F. Linear systems with polynomials of filtered Poisson processes. Probab. Eng. Mech. 12(2):1997;97-103.
19. Papadimitriou C., Katafygiotis L.S., Lutes L.D. Response cumulants of nonlinear systems subject to external and multiplicative excitations. Probab. Eng. Mech. 14(1-2):1999;149-160.
20. Di Paola M., Falsone G. Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes. J. Appl. Mech. ASME. 60:1993;141-148.
21. L.D. Lutes, C. Papadimitriou, Finding response cumulants for nonlinear systems with multiplicative excitations, Proceedings of the IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics, Madras, India, 1999, to appear.
22. R.L. Stratonovich, Topics in the Theory of Random Noise. (Transl. from the Russian by Silverman, R.A.) Gordon and Breach, New York, 1963.
23. Lutes L.D. State space analysis of stochastic response cumulants. Probab. Eng. Mech. 1(2):1986;94-98.
24. Crandall S.H. Non-Gaussian closure for random vibration excitation. Int. J. Non-Linear Mech. 15:1980;303-313.
25. Wu W.F., Lin Y.K. Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations. Int. J. Non-Linear Mech. 19:1984;349-362.
26. G. Muscolino, Response of linear and nonlinear structural systems under Gaussian and non-Gausssian inputs, in: F. Casciati (Ed.), Dynamic Motion and Chaotic Stochastic Behavior, Springer Verlag, Wien, Berlin, 1993.
27. Papadimitriou C. Stochastic response cumulants of MDOF linear systems. J. Eng. Mech. ASCE. 121(11):1995;1181-1192.
28. Wong E., Zakai M. On the relation between ordinary and stochastic differential equations. Int. J. Eng. Sci. 3:1965;213-229.
29. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, Springer, New York, 1990.