A technique note of exact stationary solutions on nonlinear systems under stochastic parametric excitations

Forschung im Ingenieurwesen/Engineering Research

Volumn 66, Issue 6, 2001, Pages 241-246

  Wang, R ^a   Zhang, Z ^b  

^a DONGHUA UNIVERSITY   (China)

^b Shanghai Post Telecommunication T   (China)

Author keywords

[No Author keywords available]

Indexed keywords

GAUSSIAN NOISE (ELECTRONIC); PROBABILITY; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; WHITE NOISE;

NONLINEAR STOCHASTIC SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0012676035     PISSN: 00157899     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100100100062     Document Type: Article

References (24)

1. Fuller AT (1969) Analysis of nonlinear stochastic systems by means of the Fokker-Plank equation. Int. J. Control 9, 603-655
2. Caughey TK, Ma F (1982) The steady-state response of a class of dynamical systems to stochastic excitation. J. Appl. Mech. 49, 629-632
3. Caughey TK, Ma F (1982) Exact steady-state solutions of a class of nonlinear stochastic systems. Int. J. Nonlinear Mech. 17(3), 137-142
4. Dimentberg MF (1982) An exact solution to a certain nonlinear random vibration problem. Int. J. Nonlinear Mech. 17, 231-236
5. Yong Y, Lin YK (1987) Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations. J. Appl. Mech. ASME 55, 702-705
6. Lin YK, Cai GQ (1988) Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations. Part II. J. Appl. Mech. ASME 55, 702-705
7. Zhu WQ (1990) Exact solutions for stationary response of several classes of nonlinear systems to parametric and/or external white noise excitations. Appl. Math. Mech. 11, 165-175
8. Wang R, Kusumoto S, Zhang Z (1996) Exact stationary response solutions of nonlinear dynamic systems. Arch. Appl. Mech. 66, 255-263
9. Wang R, Yasuda K (1997) Exact stationary probability density for second-order nonlinear systems under external white noise excitation. J. Sound and Vibration 205(5), 647-655
10. Wang R, Yasuda K, Zhang Z (2000) An generalized analysis technique of the stationary FPK equation in nonlinear stochastic systems under Gaussian white noise excitation. Int. J. Eng. Sci. 38, 1315-1330
11. Wang R, Zhang Z (1998) Exact stationary response solutions of six classes of nonlinear stochastic systems under stochastic parametric and external excitations. J. Eng. Mech. ASCE 18, 18-23
12. Straonovich RL (1963) Topics in the theory of random noise, Vol. 1. Gordon and Breach, New York
13. Bruckner A, Lin YK (1987) Application of complex stochastic averaging to non-linear random vibration problems. Int. J. Non-Linear Mech. 22(3), 237-250
14. Cai GQ, Lin YK, Elishakoff I (1992) A new approximate solution technique for randomly excited nonlinear oscillators-II. Int. J. Non-Linear Mech. 27(6), 969-979
15. Cai GQ, Lin YK (1992) A new approximate solution technique for randomly excited nonlinear oscillators. Int. J. Non-Linear Mech. 23(5/6), 409-420
16. Zhou S (1995) A mathematical model applied in the analysis of nonlinear vibration. Shanghai J. Mech. 16(4), 353-367
17. Suzuki R, Yasuda K (1998) Self-excited vibrations induced by friction between rubber and glass in sliding contact. Proceeding, Dynamics and Design Conference (Japanese), pp. 285-288
18. Xu Z, Tamura H, Seto K (1998) On the chaotic vibration of a repulsive maglev vehicle with secondary suspension. Proceeding, Dynamics and Design Conference (Japanese), pp. 315-318
19. Zhang Z, Wang R, Yasuda K (1998) On joint stationary probability density function of nonlinear dynamic systems. Acta Mechanica 130, 29-39
20. Soong TT (1973) Random differential equations in science and engineering. Academic Press, New York and London
21. Lin YK (1967) Probabilistic theory of structural dynamics. McGraw-Hill Book Company
22. Soize C (1991) Exact stationary responses of Multi-Dimensional nonlinear Hamiltonian dynamical systems under parametric and external stochastic excitations. J. Sound and Vibration 149, 1-24
23. Soize C (1988) Steady-state solution of Fokker-Planck equation in high dimension. Probabilistic Eng. Mech. 3, 196-206
24. Wang R, Yasuda K (1997) Stationary probability density of class of non-linear dynamical systems to stochastic excitation Forschung im Ingenieurwesen 63(5), 158-160