Multi-Gaussian closure method for randomly excited non-linear systems

International Journal of Non-Linear Mechanics

Volumn 33, Issue 2, 1998, Pages 201-214

  Er, Guo Kang ^a  

^a NONE

Author keywords

FPK equation; Multi Gaussian closure; Non linear random systems

Indexed keywords

EID: 0001209593     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7462(97)00018-8     Document Type: Article

References (27)

1. H. A. Kramers, Brownian motion in a field of force and diffusion model of chemical reactions. Physica 7, 284-304 (1940).
2. T. K. Caughey and F. Ma, The exact steady-state solution of a class of non-linear stochastic systems. Int. J. Non-Linear Mech. 17, 137-142 (1982).
3. M. F. Dimentberg, An exact solution to a certain non-linear random vibration problem. Int. J. Non-linear Mech. 17, 231-236 (1982).
4. Y. Yong and Y. K. Lin, Exact stationary-response solution for second-order non-linear systems under parametric and external white-noise excitations. J. Appl. Mech. ASME 54, 414-418 (1987).
5. Y. K. Lin and G. Q. Cai, Exact stationary-response solution for second-order non-linear systems under parametric and external white-noise excitations: Part II. J. Appl. Mech. ASME 55, 702-705 (1988).
6. T. K. Caughey, Response of a non-linear string to random loading. J. Appl. Mech. ASME 26, 341-344 (1959).
7. T. K. Caughey, Response of van der Pol oscillator to random excitation. J. Appl. Mech. ASME 26, 345-348 (1959).
8. Y. K. Lin, Probabilistic Theory of Structural Dynamics. McGraw-Hill, New York (1967).
9. P. D. Spanos, Stochastic linearization in structural dynamics. Appl. Mech. Review 34, 1-8 (1981).
10. J. B. Roberts and P. D. Spanos, Random Vibration and Statistical Linearization. Wiley, New York (1990).
11. R. N. Iyengar and P. K. Dash, Study of the random vibration of non-linear systems by the Gaussian closure technique. J. Appl Mech. ASME 45, 393-399 (1978).
12. S. A. Assaf and L. D. Zirkie, Approximate analysis of non-linear stochastic systems. Int. J. Control 23, 477-492 (1976).
13. S. H. Crandall, Non-Gaussian closure for random vibration of non-linear oscillators. Int. J. Non-linear Mech. 15, 303-313 (1980).
14. N. C. Hampl and G. I. Schuëller, Probability densities of the response of non-linear substitutes under stochastic dynamic excitation. Prob. Engng Mech. 4, 2-9 (1989).
15. M. Grigoriu, A consistent closure method for nonlinear random vibration. Int. J. Non-Linear Mech. 26, 857-866 (1991).
16. T. T. Soong and M. Grigoriu, Random Vibration of Mechanical and Structural Systems, p. 235 Prentice Hall, New Jersey (1992).
17. G. Q. Cai and Y. K. Lin, A new approximate solution technique for randomly excited non-linear oscillators. Int. J. Non-Linear Mech. 23, 409-420 (1988).
18. G. Q. Cai, Y. K. Lin and I. Elishakoff, A new approximate solution technique for randomly excited non-linear oscillators - II. Int. J. Non-Linear Mech. 27, 969-979 (1992).
19. J. B. Roberts and P. D. Spanos, Stochastic averaging: an approximate method of solving random vibration problems. Int. J. Non-Linear Mech. 21, 111-134 (1986).
20. W. F. Wu and Y. K. Lin, Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations. Int. J. Non-Linear Mech. 19, 349-362 (1984).
21. R. A. Ibrahim, A. Soundararajan and H. Heo, Stochastic response of non-linear dynamic systems based on a non-Gaussian closure. J. Appl. Mech. ASME 52, 965-970 (1985).
22. A. M. Hasofer and M. Grigoriu, A new perspective on the moment closure method. J. Appl. Mech. ASME 62, 527-532 (1995).
23. J.-Q. Sun and C. S. Hsu, Cumulant-neglect closure method for non-linear systems under random excitations. J. Appl. Mech. ASME 54, 649-655 (1987).
24. S. H. Crandall, Perturbation techniques for random vibration of nonlinear systems. J. Acoust. Soc. Am. 35, 1700-1705 (1963).
25. T. T. Soong, Random Differential Equations in Science and Engineering. Academic Press, New York (1973).
26. E. Wong and M. Zakai, On the relation between ordinary and stochastic equations. Int. J. Engng Sci. 3, 213-229 (1965).
27. Y. K. Lin and G. Q. Cai, Probabilistic Structural Dynamics, p. 171. McGraw-Hill, New York (1995).