Response probability density functions of strongly non-linear systems by the path integration method

International Journal of Non-Linear Mechanics

Volumn 41, Issue 5, 2006, Pages 693-705

  Iourtchenko, Daniil V ^a   Mo, Eirik ^b   Naess, Arvid ^b  

^a RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Control; Path integration; Probability density function; Random vibrations; Strongly non linear systems; Swings; Upcrossing rate

Indexed keywords

FUNCTION EVALUATION; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

PATH INTEGRATION; RANDOM VIBRATIONS; STRONGLY NONLINEAR SYSTEMS; UPCROSSING RATE;

NONLINEAR SYSTEMS;

EID: 33745863500     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2006.04.002     Document Type: Article

References (27)

1. Lin Y.K., and Cai G.Q. Probabilistic Structural Dynamics (1995), McGraw-Hill, New York
2. Dimentberg M.F. An exact solution to a certain non-linear random vibration problem. Int. J. Non-linear Mech. 17 4 (1982) 231-236
3. Proppe C. Exact stationary probability density functions for non-linear systems under Poisson white noise excitation. Int. J. Non-linear Mech. 38 (2003) 557-564
4. Vasta M. Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process. Int. J. Non-linear Mech. 30 4 (1995) 407-418
5. Dimentberg M.F. Statistical Dynamics of Nonlinear and Time-Varying Systems (1988), Research Studies Press, Taunton, UK
6. Krenk S., and Roberts J.B. Local similarity in non-linear random vibration. ASME J. Appl. Mech. 66 1 (1989) 225-236
7. Hampl N.C., and Schueller G.I. Probability densities of the response of nonlinear structures under stochastic dynamic excitation. Probab. Eng. Mech. 4 1 (1989) 2-9
8. Roberts J.B., and Spanos P.D. Random Vibration and Statistical Linearization (1990), Wiley, New York
9. Pradlwarter H.J. Non-linear stochastic response distributions by local statistical linearization. Int. J. Non-linear Mech. 36 7 (2001) 1135-1151
10. Crandall S.H. On using non-Gaussian distributions to perform statistical linearization. Int. J. Non-linear Mech. 39 9 (2004) 1395-1406
11. Iourtchenko D.V., and Song L.L. Numerical investigation of a response probability density function of stochastic vibroimpact systems with inelastic impacts. Int. J. Non-linear Mech. 41 (2006) 447-455
12. Schueller G.I., et al. A state of-the-art report on computational stochastic mechanics. Probab. Eng. Mech. 12 4 (1997) 197-321
13. Spencer Jr. B.F., and Bergman L.A. On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems. Nonlinear Dynamics 4 (1993) 357-372
14. Bergman L.A., Wojtkiewicz S.F., Johnson E.A., and Spencer Jr. B.F. Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations. In: Kliemann W.H., Langford W.F., and Sri Namachchivaya (Eds). Fields Institute Communications: Nonlinear Dynamics and Stochastic Mechanics (1996), American Mathematical Society, Providence, RI 2337
15. Naess A., and Johnsen J.M. Response statistics of nonlinear, compliant offshore structures by the path integral solution method. Probab. Eng. Mech. 8 2 (1993)
16. Naess A., and Moe V. Efficient path integration methods for nonlinear dynamic systems. Probab. Eng. Mech. 15 2 (2000) 221-231
17. A. Masud, L.A. Bergman, Solution of the four dimensional Fokker-Planck equation: still a challenge, Nonlinear Dynamics, vol. 4, Proceedings of ICOSSAR Conference, 2005, 328pp.
18. Iourtchenko D.V., and Dimentberg M.F. Energy balance for random vibration of piecewise-conservative systems. J. Sound Vibration 248 5 (2001) 913-923
19. Dimentberg M.F., and Bratus A.S. Bounded parametric control of random vibrations. Proc. R. Soc., Ser. A 456 (1989) 2351-2363
20. Panovko Y.G., and Guanova I.I. PStability and Oscillations of Elastic Systems: Paradoxes, Fallacies, and New Concepts (1965), Consultants Bureau, New York
21. Iourtchenko D.V. Stochastic control of mathematical pendulum by moment of inertia. J. Comput. System Sci. Int. 43 1 (2004) 79-83
22. Khasminskii R.Z. A limit theorem for solution of differential equations with random right-hand-side. J. Probab. Appl. 11 3 (1966) 390-405
23. Dimentberg M.F. On the theory of swings. J. Vibration Control 8 (2002) 311-319
24. C. Boor, A Practical Guide to Splines, Springer Applied Mathematical Sciences, vol. 27, 2001.
25. Soong T.T., and Grigoriu M. Random Vibration of Mechanical and Structural Systems (1997), Prentice-Hall, Inc., NJ, USA
26. D.V. Iourtchenko, A. Naess, E. Mo, Response PDF of a stiffness-controlled system by the path integration method, ENOC 2005, 2005.
27. Leung H.K. Stochastic transient of a noisy van der Pole oscillator. Physica A 221 (1995) 340-347