Stochastic averaging of quasi-linear systems driven by Poisson white noise

Probabilistic Engineering Mechanics

Volumn 25, Issue 1, 2010, Pages 99-107

  Zeng, Y ^a   Zhu, W Q ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Perturbation method; Poisson white noise; Quasi linear system; Stochastic averaging

Indexed keywords

ENERGY DEPENDENT; EXCITATION PROCESS; FOKKER-PLANCK-KOLMOGOROV; FPK EQUATION; MONTE CARLO SIMULATION; NONGAUSSIANITY; NUMERICAL RESULTS; PERTURBATION METHOD; PERTURBATION SOLUTIONS; POISSON WHITE NOISE; POWER LAW; PROBABILITY DENSITIES; QUASI-LINEAR SYSTEM; RAYLEIGH OSCILLATORS; SINGLE-DEGREE-OF-FREEDOM; STATIONARY SOLUTIONS; STOCHASTIC AVERAGING; TOTAL ENERGY; VAN DER POL OSCILLATOR;

CIRCUIT OSCILLATIONS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; DAMPING; LINEAR SYSTEMS; MONTE CARLO METHODS; POISSON DISTRIBUTION; POISSON EQUATION; WHITE NOISE;

PERTURBATION TECHNIQUES;

EID: 70349975725     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2009.08.003     Document Type: Article

References (35)

1. Kim K.I., Powers E.J., et al. Modeling of the nonlinear drift-oscillations of moored vessels subject to non-gaussian random sea-wave excitation. IEEE J Ocean Eng 12 4 (1987) 568-575
2. Moshchuk N., and Ibrahim R.A. Response statistics of ocean structures to non-linear hydrodynamic loading. 2. Non-Gaussian ocean waves. J Sound Vibration 191 1 (1996) 107-128
3. Ko N.H., You K.P., et al. The effect of non-Gaussian local wind pressures on a side face of a square building. J Wind Eng Ind Aerodyn 93 5 (2005) 383-397
4. Grigoriu M. Equivalent linearization for Poisson white-noise input. Probab Eng Mech 10 1 (1995) 45-51
5. Sobiechowski C., and Socha L. Statistical linearization of the duffing oscillator under non-Gaussian external excitation. J Sound Vibration 231 1 (2000) 19-35
6. Proppe C. Equivalent linearization of MDOF systems under external Poisson white noise excitation. Probab Eng Mech 17 4 (2002) 393-399
7. Proppe C. Stochastic linearization of dynamical systems under parametric Poisson white noise excitation. Int J Non-Linear Mech 38 4 (2003) 543-555
8. Cai G.Q., and Suzuki Y. Response of systems under non-Gaussian random excitations. Nonlinear Dyn 45 1-2 (2006) 95-108
9. Cai G.Q., and Lin Y.K. Response distribution of nonlinear-systems excited by non-Gaussian impulsive noise. Int J Non-Linear Mech 27 6 (1992) 955-967
10. Wu Y., and Zhu W.Q. Stationary response of MDOF dissipated hamiltonian systems to poisson white noises. J Appl Mech-Trans ASME 75 4 (2008)
11. Wu Y., and Zhu W.Q. Stationary response of multi-degree-of-freedom vibro-impact systems to Poisson white noises. Phys Lett A 372 5 (2008) 623-630
12. Koyluoglu H.U., Nielsen S.R.K., et al. Fast cell-to-cell mapping (path integration) for nonlinear white-noise and Poisson driven systems. Struct Saf 7 3 (1995) 151-165
13. Di Paola M., and Santoro R. Path integral solution for non-linear system enforced by Poisson White Noise. Probab Eng Mech 23 2-3 (2008) 164-169
14. Wu Y., and Zhu W.Q. Stochastic analysis of a pulse-type prey-predator model. Phys Rev E 77 4 (2008)
15. Di Paola M., and Santoro R. Non-linear systems under Poisson white noise handled by path integral solution. J Vib Control 14 1-2 (2008) 35-49
16. Wojtkiewicz S.F., Johnson E.A., et al. Response of stochastic dynamical systems driven by additive Gaussian and Poisson white noise: Solution of a forward generalized Kolmogorov equation by a spectral finite difference method. Comput Meth Appl Mech Eng 168 1-4 (1999) 73-89
17. Di Paola M., and Falsone G. Stochastic dynamics of non-linear systems driven by non-normal delta-correlated processes. J Appl Mech-Trans Asme 60 (1993) 141-148
18. Di Paola M., and Falsone G. Itô and Stratonovich integrals for delta-correlated processes. Probab Eng Mech 8 (1993) 197-208
19. Hu S.L.J. Responses of dynamic-systems excited by non-Gaussian pulse processes. J Eng Mech-ASCE 119 9 (1993) 1818-1827
20. Hu S.L.J. Parametric random vibrations under non-Gaussian delta-correlated processes. J Eng Mech-ASCE 121 12 (1995) 1366-1371
21. Muscolino G. Linear-systems excited by polynomial forms of non-Gaussian filtered processes. Probab Eng Mech 10 1 (1995) 35-44
22. Grigoriu M. A partial differential equation for the characteristic function of the response of non-linear systems to additive Poisson white noise. J Sound Vibration 198 2 (1996) 193-202
23. Grigoriu M. Characteristic function equations for the state of dynamic systems with Gaussian, Poisson, and Levy white noise. Probab Eng Mech 19 4 (2004) 449-461
24. Orabi II, and Ahmadi G. Response of the duffing oscillator to a non-Gaussian random-excitation. J Appl Mech-Trans ASME 55 3 (1988) 740-743
25. Grigoriu M. Linear and nonlinear-systems with non-Gaussian white-noise input. Probab Eng Mech 10 3 (1995) 171-179
26. Grigoriu M. Response of dynamic systems to Poisson white noise. J Sound Vibration 195 3 (1996) 375-389
27. Proppe C. The Wong-Zakai theorem for dynamical systems with parametric Poisson white noise excitation. Internat J Engrg Sci 40 10 (2002) 1165-1178
28. Iwankiewicz R. Dynamical systems with multiplicative random impulse process excitation. In: Namachchivaya N.Sri., and Lin Y.K. (Eds). IUTAM symposium on nonlinear stochastic dynamics (2003), Klumer Academic Publishers, Netherlands 343-352
29. Grigoriu M. The Itô and Stratonovich integrals for stochastic differential equations with Poisson white noise. Probab Eng Mech 13 3 (1998) 175-182
30. Roberts J.B., and Spanos P.D. Stochastic averaging: An approximate method of solving random vibration problems. Internat J Non-Linear Mech 21 (1986) 111-134
31. Zhu W.Q. Stochastic averaging methods in random vibration. Appl Mech Rev 41 5 (1988) 189-199
32. Zhu W.Q. Recent developments and applications of the stochastic averaging method in random vibration. Appl Mech Rev 49 10 (1996) s72-s80
33. Zhu W.Q. Nonlinear Stochastic dynamics and control in Hamiltonian formulation. Appl Mech Rev 59 1-6 (2006) 230-248
34. Huang Z.L., and Zhu W.Q. stochastic averaging of quasi-generalized Hamiltonian systems. Internat J Non-Linear Mech 44 (2009) 71-80
35. Stratonovich R.L. Topics in the theory of random noise, Vol. 1 (1963), Gordon and Breach, New York