Exact stationary solutions of the Fokker-Planck equation for nonlinear oscillators under stochastic parametric and external excitations

Nonlinearity

Volumn 13, Issue 3, 2000, Pages 907-920

  Wang, Rubin ^a   Zhang, Zhikang ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b Shanghai Post Telecommunication T   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034178886     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/3/322     Document Type: Article

References (36)

1. Fuller A T 1969 Analysis of nonlinear stochastic systems by means of the Fokker-Planck equation Int. J. Control 9 603-55
2. Lin Y K and Cai G Q 1988 Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations: part II J. Appl. Mech. ASME 55 702-5
3. Caughey T K and Ma F 1982 The steady-state response of a class of dynamical systems to stochastic excitation J. Appl. Mech. 49 629-32
4. Caughey T K and Ma F 1982 Exact steady-state solutions of a class of nonlinear stochastic systems Int. J. Nonlinear Mech. 17 137-42
5. Dimentberg M F 1982 An exact solution to a certain nonlinear random vibration problem Int. J. Nonlinear Mech. 17 231-6
6. Yong Y and Lin Y K 1987 Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations J. Appl. Mech. ASME 55 702-5
7. Soize C 1988 Steady-state solution of Fokker-Planck equation in high dimension Prob. Eng. Mech. 3 196-206
8. Soize C 1991 Exact stationary responses of multi-dimensional nonlinear Hamiltonian dynamical systems under parametric and external stochastic excitations J. Sound Vib. 149 1-24
9. Zhu W Q 1990 Exact solutions for stationary response of several classes of nonlinear systems to parametric and/or external white noise excitations Appl. Math. Mech. 11 165-75
10. Zhu W Q, Cai G Q and Lin Y K 1990 Exact stationary solutions of stochastically perturbed Hamiltonian systems Prob. Eng. Mech. 5 84-7
11. Zhu W Q, Cai G Q and Lin Y K 1992 Stochastically excited Hamiltonian systems Nonlinear Stochastic Mechanics ed N Bellomo and F Casiati (Berlin: Springer) pp 543-52
12. Lin Y K and Cai G Q 1995 Probabilistic structural dynamics Advanced Theory and Applications (New York: McGraw-Hill)
13. Zhu W Q and Yang Y Q 1996 Exact stationary solutions of stochastically excited and dissipated integrable hamiltonian systems J. Appl Mech., Trans. ASME 63 493-500
14. Wang R and Yasuda K 1997 Exact stationary probability density for second-order nonlinear systems under external white noise excitation J. Sound Vib. 205 647-55
15. Wang R and 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
16. Cai G Q and Lin Y K 1996 Exact and approximate solutions for randomly excited MDOF non-linear systems Int. J. Non-Linear Mech. 31 647-55
17. Nigam N C 1983 Introduction to Random Vibrations (Cambridge, MA: MIT Press)
18. Wang R, Yasuda K and Zhang Z 2000 A generalized analysis technique of the stationary FPK equation under white noise excitations Int. J. Eng. Sci. 38 1315-30
19. Straonovich R L 1963 Topics in the Theory of Random Noise vol 1 (New York: Gordon and Breach)
20. Zhang Z, Wang R and Yasuda K 1998 On joint stationary probability density function of nonlinear dynamic systems Acta Mechanica 130 29-39
21. Bruckner A and Lin Y K 1987 Application of complex stochastic averaging to non-linear random vibration problems Int. J. Non-Linear Mech. 22 237-50
22. Cai G Q, Lin Y K and Elishakoff 1992 A new approximate solution technique for randomly excited non-linear oscillators-II Int. J. Non-Linear Mech. 27 969-79
23. Cai G Q and Lin Y K 1992 A new approximate solution technique for randomly excited non-linear oscillators Int. J. Non-Linear Mech. 23 409-20
24. Zhou S 1995 A mathematical model applied in the analysis of nonlinear vibration Shanghai J. Mech. 16 353-67
25. Suzuki R and Yasuda K 1998 Self-excited vibrations induced by friction between rubber and glass in sliding contact Proc. Dynamics and Design Conf. (Japan) pp 285-8
26. Xu Z, Tamura H and Seto K 1998 On the chaotic vibration of a repulsive maglev vehicle with secondary suspension Proc. Dynamics and Design Conf. (Japan) pp 315-8
27. Soon T T 1973 Random Differential Equations in Science and Engineering (New York: Academic)
28. Lin Y K 1967 Probabilistic Theory of Structural Dynamics (New York: McGraw-Hill)
29. Gardiner C W 1985 Handbook of Stochastic Methods 2nd edn (Berlin: Springer)
30. Risken H 1989 The Fokker-Planck Equation 2nd edn (Berlin: Springer)
31. Soize C 1994 The Fokker-Planck Equation for Stochastic Dynamical Systems and its Explicit Steady State Solutions (Singapore: World Scientific)
32. Wang R, Kusumoto S and Zhang Z 1996 Exact Stationary Response Solutions of Nonlinear Dynamic Systems (Archive of Applied Mechanics vol 66) (Berlin: Springer) pp 255-63
33. Wang R, Yasuda K and Zhang Z 2000 A proposal of testing method on the exact steady state probability density function of nonlinear stochastic systems J. Sound Vib. accepted
34. Wang R, Kusumoto S and Zhang Z 1996 A new equivalent nonlinearization method Probab. Eng. Mech. 11 129-37
35. Wang R, Kusumoto S and Zhang Z 1995 An equivalent polynomial approximation technique in nonlinear structural dynamics Arch. Appl. Mech. 65 457-64
36. Wang R and Yasuda K 1997 Stationary probability density of a class of non-linear dynamical systems to stochastic excitation Forsch. Ing. 63 158-60