Stochastic linearization of dynamical systems under parametric Poisson white noise excitation

International Journal of Non-Linear Mechanics

Volumn 38, Issue 4, 2003, Pages 543-555

  Proppe, Carsten ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Parametrical excitation; Poisson white noise; Stochastic linearization

Indexed keywords

DIFFERENTIAL EQUATIONS; LINEARIZATION; OSCILLATORS (ELECTRONIC); RANDOM PROCESSES; WHITE NOISE;

PARAMETRIC EXCITATIONS;

NONLINEAR SYSTEMS;

EID: 0037408865     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(01)00083-X     Document Type: Article

References (22)

1. Falsone G. Stochastic linearization of MDOF systems under parametric excitation. Int. J. Non-Linear Mech. 27(6):1992;1025-1037.
2. L. Sperling, Analytische Näherungsmethoden zur Untersuchung nichtlinearer, stochastisch erregter Systeme, Habilitationssschrift, Technische Hochschule Otto von Guericke, Magdeburg, März 1979.
3. Chang R.J., Young G.E. Methods and Gaussian criterion for statistical linearization of stochastic parametrically and externally excited nonlinear systems. Trans. ASME, J. Appl. Mech. 56:1989;179-185.
4. Kottalam J., Lindenberg K., West B.J. Statistical replacement for systems with delta-correlated fluctuations. J. Statist. Phys. 42(5/6):1986;979-1009.
5. Brückner A., Lin Y.K. Generalization of the equivalent linearization method for non-linear random vibration problems. Int. J. Non-Linear Mech. 22(3):1987;227-235.
6. Wu W.-F. Comparison of Gaussian closure technique and equivalent linearization method. Prob. Eng. Mech. 2(1):1987;2-8.
7. L. Socha, Probability density equivalent linearization technique for nonlinear oscillator with stochastic excitations, Z. Angew. Math. Mech., in press.
8. Kozin F. The method of statistical linearization for non-linear stochastic vibrations. Ziegler F., Schuëller G.I. Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamic Engineering Systems. 1988;45-56 Springer, Berlin, Heidelberg, New York.
9. Lin Y.K. Nonstationary exciation and response in linear systems treated as random impulses. J. Acoust. Soc. Am. 38:1965;453-460.
10. Roberts J.B. The response of linear vibratory systems to random impulses. J. Sound Vibr. 2:1965;375-390.
11. Śniady P. Dynamic response of linear structures to a random stream of impulses. J. Sound Vibr. 131(1):1989;91-102.
12. F. Casciati, M. Di Paola, Stochastic process models, in: F. Casciati, B. Roberts (Eds.), Mathematical Models for Structural Reliability Analysis, CRC Press, Boca Raton, FL, 1996, 1-50 (Chapter 1).
13. M. Di Paola, Stochastic differential calculus, in: F. Casciati (Ed.), Dynamic Motion: Chaotic and Stochastic Behaviour, Springer, Wien, New York, 1993, pp. 29-92 (Chapter 2).
14. Di Paola M., Falsone G. Itô and Stratonovich integrals for delta-correlated processes. Prob. Eng. Mech. 8:1993;197-208.
15. Di Paola M., Falsone G. Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes. Trans. ASME, J. Appl. Mech. 60:1993;141-148.
16. Gichman I., Skorochod A. Stochastische Differentialgleichungen. 1971;Akademie-Verlag, Berlin.
17. Snyder D.L. Random Point Processes. 1975;Wiley, New York.
18. Di Paola M., Vasta M. Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses. Int. J. Non-Linear Mech. 32(5):1997;855-862.
19. Sakata R., Kimura K. Calculation of the non-stationary mean square response of a non-linear system subjected to non-white excitation. J. Sound Vibr. 73(3):1980;333-344.
20. Pradlwarter H.J., Li W. On the computation of the stochastic response of highly nonlinear large MDOF-systems modeled by finite elements. Prob. Eng. Mech. 6(2):1991;109-116.
21. Spanos P.-T.D., Iwan W.D. On the existence and uniqueness of solutions generated by equivalent linearization. Int. J. Non-Linear Mech. 13:1978;71-78.
22. Roberts J.B., Spanos P.D. Random Vibration and Statistical Linearization. 1990;Wiley, Chichester.