Linear systems excited by polynomials of filtered poisson pulses

Journal of Applied Mechanics, Transactions ASME

Volumn 64, Issue 3, 1997, Pages 712-717

  Di Paola, M ^a  

^a UNIVERSITY OF PALERMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000940513     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2788955     Document Type: Article

References (24)

1. Arnold, L., 1973, Stochastic differential equations: Theory and applications, John Wiley and Sons, New York.
2. Di Paola, ML, 1993, Stochastic differential calculus (CISM Courses and Lectures No. 340), Casciati, ed., Springer-Verlag, New York, pp. 29-92.
3. Di Paola, M., and Falsone, G., 1993, “Ito and Stratonovich integral for delta correlated processes,” Probabilistic Engineering Mechanics, Vol. 8, pp, 197-208.
4. Di Paola, M., and Falsone, G., 1993, “Stochastic Dynamics of Nonlinear Systems Driven by Non-Normal Delta Correlated Processes,” ASME Journal of Applied Mechanics, Vol. 60, pp. 141-148.
5. Di Paola, M., and Falsone, G., 1994, “Nonlinear oscillators under parametric and external Poisson pulses,” Nonlinear Dynamics, Vol. 5, pp. 337-352.
6. Di Paola, M., and Muscolino, G., 1990, “Differential moment equations of FE modelled structures with geometrical non-linearities,” Int. Journal of Nonlinear Mechanics, Vol. 25, No. 4, pp. 363-373.
7. Di Paola, M., Falsone, G., and Pirrotta, A., 1992, “Stochastic response analysis of non-linear systems under Gaussian inputs,” Probabilistic Engineering Mechanics, Vol. 7, pp. 15-21.
8. Dimentberg, M. F., 1988, Statistical dynamics of nonlinear and time-varying systems, Research Studies Press, U.K.
9. Gardiner, C. W., 1985, Handbook of stochastic methods, Springer-Verlag, New York.
10. Grigoriu, M., 1987, “White noise processes,” Journal of Engineering Mechanics, Vol. 113, No. 5, pp. 757-765.
11. Grigoriu, M., and Ariaratnam, S.T., 1988, “Response of Linear Systems to Polynomials of Gaussian Processes,” ASME Journal of Applied Mechanics, Vol. 55, pp. 905-910.
12. Grigoriu, M., Wall, W. A., and Bucher, C. G., 1995, “A novel algorithm for analyzing non linear systems by perturbation theory,” Computational Stochastic Mechanics, P. D. Spanos, Ed., Balkema, Rotterdam.
13. Ibrahim, R. A., 1985, Parametric random vibration, John Wiley and Sons, New York.
14. Ito, K., 1951, “On a formula concerning stochastic differential equation,” Nagoya Mathematical Journal, Vol. 3, pp. 55-65.
15. Iwankiewicz, R., Nielsen, S. R. K., and Christensen, P. T., 1990, “Dynamic response of non-linear systems to Poisson distributed pulse train Markov approach,” Nonlinear Structural System under Random Conditions, F. Casciati, I. Elishakoff, and J. B. Roberts, eds., pp. 223-238.
16. Lin, Y. K;, 1965, “Non stationary excitation and response in linear systems treated on sequence of random pulses,” Journal of the Acoustical Society of America, Vol. 38, pp. 453-460.
17. Lutes, L. D., 1986, “Cumulants of Stochastic Response for Linear Systems,” ASME Journal of Applied Mechanics, Vol. 112, No. 10, pp. 1062-1075.
18. Lutes, L. D., and Hu, S.-L., 1986, “Non-Normal Stochastic Response of Linear Systems,” ASME Journal of Applied Mechanics, Vol. 112, No. 2, pp. 127141.
19. Muscolino, G., 1995, “Linear systems excited by polynomial form of non-Gaussian filtered processes,” Probabilistic Engineering Mechanics, Vol. 10, pp. 35-44.
20. Roberts, J. B., 1972, “Systems response to random impulses,” Journal of Sound and Vibration, Vol. 24, pp. 23-34.
21. Rugh, W. J., 1981, Non linear system theory: The Volterra/Wiener approach, John Hobkins Press Ltd., London.
22. Soong, T. T., and Grigoriu, M., 1993, Random vibration of mechanical and structural systems, PTR, Prentice-Hall, Englewoods Cliffs, NJ.
23. Stratonovich, R. L., 1963, Topics in the theory of random noise, Vol. 1, Gordon and Breach, New York.
24. Wong, E., and Zakai, M., 1965, “On the relation between ordinary and stochastic differential equations,” Int. Journal of Engineering Sciences, Vol. 3, pp. 213-229.