Nonlinear stochastic dynamics, chaos, and reliability analysis for a single degree of freedom model of a rotor blade

Journal of Engineering for Gas Turbines and Power

Volumn 131, Issue 1, 2009, Pages

  Kumar, Pankaj ^a   Narayanan, S ^b  

^a BHARAT HEAVY ELECTRICALS LIMITED   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Blade vibration; Chaos; Finite element method; Fokker Planck equation; Nonlinear stochastic dynamics; Path integral; Reliability

Indexed keywords

BLADE VIBRATIONS; CHAOS; FINITE ELEMENT; NONLINEAR STOCHASTIC DYNAMICS; PATH INTEGRAL;

CHAOS THEORY; CONTROL NONLINEARITIES; EQUATIONS OF MOTION; EQUATIONS OF STATE; FINITE ELEMENT METHOD; FOKKER PLANCK EQUATION; FUNCTION EVALUATION; NONLINEAR SYSTEMS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; QUALITY ASSURANCE; QUANTUM THEORY; RELIABILITY ANALYSIS; ROTORS (WINDINGS); STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TIMING JITTER;

NONLINEAR EQUATIONS;

EID: 78149369667     PISSN: 07424795     EISSN: 15288919     Source Type: Journal    
DOI: 10.1115/1.2967720     Document Type: Article

References (26)

1. Srinivasan, A. V., 1997, "Flutter and Resonant Vibration Characteristics of Engine Blade," ASME J. Eng. Gas Turbines Power, 119(4), pp. 742-775.
2. Griffin, J. H., and Hoosac, T. M., 1984, "Model Development and Statistical Investigation of Turbine Blade Mistuning," ASME J. Vib., Acoust., Stress, Reliab. Des., 106, pp. 204-210.
3. Cha, D. and Sinha, A., 1999, "Statistics of Response of a Mistuned Baded Disk Assembly Subjected to White Noise and Narrow Band Excitation," ASME J. Eng. Gas Turbines Power, 119, pp. 710-717.
4. Bread, C., Green, J. S., Vahdati, M., and Imregun, M., 2001, "A Non-Linear Integrated Aeroelasticity Method for the Prediction of Turbine Forced Response With Friction Damper," Int. J. Mech. Sci., 43, pp. 2715-2736.
5. Sunderrajan, P., and Noah, S. T., 1997, "Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method-Application to Rotor Systems," ASME J. Vibr. Acoust., 119, pp. 9-20.
6. Sogliero, G., and Srinivasan, A. V., 1980, "Fatigue Life Estimates of Mistuned Blades Via a Stochastic Approach," AIAA J., 18(83), pp. 318-323.
7. Roberts, J. B., and Spanos, P. D., 1990, Random Vibration and Statistical Linearization, Wiley, New York.
8. Crandall, S. H., 1963, "Perturbation Techniques for Random Vibration of Nonlinear Systems," J. Acoust. Soc. Am., 35(11), pp. 1700-1705.
9. Wojtkiewicz, S. F., and Spencer, B. F., Jr., and Bergman, L. A., 1996, "On the Cumulant-Neglect Closure Method in Stochastic Dynamics," Int. J. Non-Linear Mech., 31(3), pp. 657-684.
10. Nigam, N. C., 1983, Introduction for Random Vibration, MIT, Cambridge, MA.
11. Wehner, M. F., and Wolfer, W. G., 1983, "Numerical Evaluation of Path-Integral Solutions to Fokker-Planck Equation," Phys. Rev. A, 27(5), pp. 2663-2670.
12. Naess, A., and Moe, V., 2000, "Efficient Path Integration Method for Nonlinear Dynamics System," Probab. Eng. Mech., 15, pp. 221-231.
13. Yu, J. S., Cai, G. Q., and Lin, Y. K., 1997, "A New Path Integration Procedure Based on Gauss-Legendre Scheme," Int. J. Non-Linear Mech., 32, pp. 759- 768.
14. Lin, H. and Yim, S. C. S., 1994, "A Path Integral Procedure for the Analysis of a Noisy Nonlinear System," Proceedings of the Second International Conference on Computational Stochastic Mechanics, Spanos, Athens, June 12-15, pp. 371-377.
15. Langley, R. S., 1985, "A Finite Element Method for the Statistics of Non-Linear Random Vibration," J. Sound Vib., 101(1), pp. 41-54.
16. Spencer, B. F., and Bergman, L. A., 1991, "Numerical Solution of the Fokker-Planck Equation for First Passage Probability," Computational Stochastic Mechanics, P. D. Spanos and C. A. Brebbia, eds., Elsevier, Southampton, pp. 359-370.
17. Kumar, P., and Narayanan, S., 2006, "Solution of Fokker-Planck Equation by Finite Element and Finite Difference Methods for Nonlinear System," Sadhana: Proc., Indian Acad. Sci., 31(4), pp. 455-473.
18. Wojtkiewicz, S. F., Bergman, L. A., and Spencer, B. F., Jr., 1994, "Robust Numerical Solution of the Fokker-Planck-Kolmogorov Equation for Two Dimensional Stochastic Dynamical Systems," Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Technical Report No. AAE 94-08.
19. Kunert, A., 1991, "Efficient Numerical Solution of Multidimensional Fokker-Planck Equations With Chaotic and Nonlinear Random Vibration," Vibration Analysis: Analytical and Computational, T. C. Huang, eds., Vol. DE-37, pp. 57-60.
20. Soong, T., and Grigoriu, M., 1993, Random Vibration of Mechanical and Structural Systems, Prentice-Hall, Englewood Cliffs, NJ.
21. Wong, E., and Zakai, M., 1965, "On the Relation Between Ordinary and Stochastic Differential Equation," Int. J. Eng. Sci., 3, pp. 213-229.
22. Risken, H., 1989, The Fokker-Planck Equation: Methods of Solution and Applications, Springer-Verlag, New York.
23. Crandall, S. H., 1970, "First Crossing Probabilities of the Linear Oscillator," J. Sound Vib., 12(3), pp. 285-299.
24. Zhang, D. S., Wei, G. W., Kouri, D. J., and Hoffman, D. K., 1997, "Numerical Method for the Nonlinear Fokker-Planck Equation," Phys. Rev. E, 56(1), pp. 1197-1206.
25. Naess, A., 2000, "Chaos and Nonlinear Stochastic Dynamics," Probab. Eng. Mech., 15, pp. 37-47.
26. Jung, P., and Hänggi, P., 1990, "Invariant Measure of a Driven Nonlinear Oscillator With External Noise," Phys. Rev. Lett., 65, pp. 3365-3368.