Reliability of strongly nonlinear single degree of freedom dynamic systems by the path integration method

Journal of Applied Mechanics, Transactions ASME

Volumn 75, Issue 6, 2008, Pages 0610161-0610168

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

^a PETER THE GREAT ST PETERSBURG POLYTECHNIC UNIVERSITY   (Russian Federation)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Control; Outcrossing rate; Path integration; Probability density function; Random vibrations; Reliability; Strongly nonlinear systems; Swings

Indexed keywords

NONLINEAR SYSTEMS; PROBABILITY DENSITY FUNCTION; QUALITY ASSURANCE; RELIABILITY ANALYSIS;

OUTCROSSING RATE; PATH INTEGRATION; RANDOM VIBRATIONS; STRONGLY NONLINEAR SYSTEMS; SWINGS;

RELIABILITY;

EID: 55149091310     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2967896     Document Type: Article

References (25)

1. Dimentberg, M. F., 1988, Statistical Dynamics of Nonlinear and Time-Varying Systems, Research Studies, Taunton, UK.
2. Lin, Y. K., and Cai, G. Q., 1995, Probabilistic Structural Dynamics. McGraw-Hill, New York.
3. Roberts. J. B., and Spanos, P. D.. 1990, Random Vibration and Statistical Linearization, Wiley, New York.
4. Roberts, J. B., 1976, "First Passage Time for the Envelope of a Randomly Excited Linear Oscillator," J. Sound Vib., 46(1), pp. 1-14.
5. Roberts, J. B., 1978, "First Passage Time for Oscillators With Non-Linear Restoring Forces," J. Sound Vib., 56(1), pp. 71-86.
6. Roberts, J. B., 1978, "First Passage Time for Oscillators With Nonlinear Damping," ASME J. Appl. Mech., 45, pp. 175-180.
7. Bergman, L. A., and Heinrich, J. C., 1982, "On the Reliability of the Linear Oscillator and Systems of Coupled Oscillators," Int. J. Numer. Methods Eng., 18, pp. 1271-1295.
8. Spencer, B. F., Jr., and Bergman, L. A., 1985, "On the Reliability of a Simple Hysteretic System," J. Eng. Mech., 111(12), pp. 1502-1513.
9. Bergman, L. A., and Spencer, B. F., Jr., 1987, "First Passage Time for Linear Systems With Stochastic Coefficients," Probab. Eng. Mech., 2(1), pp. 46-53.
10. Koyluoglu, H. U., Nielsen, S. R. K., and Iwankiewicz, R., 1994, "Reliability of Non-Linear Oscillators Subjected to Poisson Driven Impulses," J. Sound Vib., 176(1), pp. 19-33.
11. Chen, J. B., and Li, J., 2005, "Dynamic Response and Reliability Analysis of Non-Linear Stochastic Structures," Probab. Eng. Mech., 20, pp. 33-44.
12. Gupta, S., and Manohar, C. S., 2004, "Improved Response Surface Method for Time-Varying Reliability Analysis of Nonlinear Random Structures Under Non-Stationary Excitations," Nonlinear Dyn., 36, pp. 267-280.
13. Zhu, W. Q., Deng, M. L., and Huang, Z. L., 2002, "First-Passage Failure of Quasi-Integrable Hamiltonian Systems," ASME J. Appl. Mech., 69, pp. 274-282.
14. Fujimura, K., and Kiureghian. A., 2007, "Tail-Equivalent Linearization Method for Nonlinear Random Vibration," Probab. Eng. Mech., 22, pp. 63-76.
15. lourtchenko, D. V., 2000. "Stochastic Optimal Bounded Control for a System With the Boltz Cost Function," J. Vib. Control, 6, pp. 1195-1204.
16. Dimentberg, M. F., lourtchenko, D. V., and Bratus, A., 2000, "Optimal Bounded Control of Steady-State Random Vibrations," Probab. Eng. Mech., 15, pp. 381-386.
17. Risken, H., 1989, The Fokker-Plank Equation: Methods of Solutions and Applications, Springer-Verlag, New York.
18. Iourtchenko D. V., and Dimentberg M. F., 2001, "Energy Balance for Random Vibrations of Piecewise-Conservative Systems," J. Sound Vib., 248(5), pp. 913-923.
19. Dimentberg, M. F., and Bratus, A.. 2000, "Bounded Parametric Control of Random Vibrations," Proc. R. Soc. London, Ser. A, 456, pp. 2351-2363.
20. Iourtchenko, D. V., 2006, "Random Vibrations of Swings," J. Sound Vib., 295, pp. 1011-1014.
21. Panovko, la. G., and Gubanova, I. I., 1965, Stability and Oscillations of Elastic Systems: Paradoxes. Fallacies, and New Concepts, Consultants Bureau, New York.
22. Iourtchenko, D. V., Mo, E.. and Naess, A., 2006, "Response Probability Density Functions of Strongly Nonlinear Systems by the Path Integration Method," Int. J. Non-Linear Mech., 41(5), pp. 693-705.
23. Johnsen, J. M.. 1992, "Response Statistics of Nonlinear Dynamic Systems," Ph.D. thesis, Department of Structural Engineering, Norwegian Institute of Technology, Trondheim.
24. Naess, A., Kolnes, F. E., and Mo, E., 2007, "Stochastic Spur Gear Dynamics by Numerical Path Integration," J. Sound Vib., 302, pp. 936-950.
25. Naess, A., and Johnsen, J. M., 1993, "The Effect of Coulomb Damping on the Response Statistics of a SDOF Oscillator Subjected to White Noise Excitation," Proceedings of the Second European Conference on Structural Dynamics (Eurodyn '93), Trondheim, Norway, Jun.