Chaotic oscillations in pipes conveying pulsating fluid

Nonlinear Dynamics

Volumn 10, Issue 4, 1996, Pages 333-357

  Jayaraman, K ^a   Narayanan, S ^b  

^a ANNA UNIVERSITY   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Chaos; Harmonic balancing; Multiple time scales; Nonlinearity; Parametric excitation; Pipes; Stability

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; EQUATIONS OF MOTION; MATHEMATICAL MODELS; NATURAL FREQUENCIES; NUMERICAL METHODS; PIPE; PIPE FLOW; PULSATILE FLOW; RESONANCE; STABILITY; VELOCITY;

CHAOTIC OSCILLATIONS; EQUILIBRIUM POINT; FLOW VELOCITY; HARMONIC BALANCING; HARMONIC VELOCITY FLUCTUATIONS; HARMONIC VELOCITY PERTURBATION; MULTIPLE TIME SCALE METHOD; SINGLE MODE APPROXIMATION; TWO MODE APPROXIMATION;

OSCILLATIONS;

EID: 0030215655     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00045481     Document Type: Article

References (26)

1. Housner, G. W., 'Bending vibrations of a pipe line containing flowing fluid', ASME Journal of Applied Mechanics 90, 1952, 205-208.
2. Niordson, F. I., 'Vibration of a cylindrical tube containing flowing fluid', Kungliga Tekniska Hogskolans Handlingar 73, 1952.
3. Paidoussis, M. P., 'Dynamics of tubular cantilevers conveying fluid', The Journal of Mechanical Engineering Science 12, 1970, 85-103.
4. Paidoussis, M. P. and Issid, N. T., 'Dynamic stability of pipes conveying fluid', Journal of Sound and Vibration 33(3), 1974, 267-294.
5. Naguleswaran, S. and Williams, C. J. H., 'Lateral vibration of a pipe conveying fluid', Journal of Mechanical Engineering Science 10, 1968, 228-238.
6. Chen, S. S., 'Dynamic stability of a tube conveying fluid', Proc. ASCE J. Eng. Mech. Div. 97, 1971, 1469-1485.
7. Ariaratnam, S. T. and Sri Namachchivaya, V., 'Dynamic stability of pipes conveying pulsating fluids', Journal of Sound and Vibration 107, 1986, 215-230.
8. Thurman, A. L. and Mote, C. D., 'Nonlinear oscillation of a cylinder containing flowing fluid', ASME J. Eng. Ind. 91, 1969, 1147-1155.
9. Holmes, P. J., 'Bifurcations to divergence and flutter in flow induced oscillations: A finite dimensional analysis', Journal of Sound and Vibration 53(4), 1977, 471-503.
10. Holmes, P. J. and Marsden, J., 'Bifurcation to divergence and flutter in flow induced oscillations: An infinite dimensional analysis', Automatica 14, 1978, 367-384.
11. Rousselet, J. and Herrmann, G., 'Flutter of articulated pipe at finite amplitude', ASME Journal of Applied Mechanics 44, 1971, 154-158.
12. Bajaj, A. K., Sethna, P. R., and Lundgren, T. S., 'Hopf bifurcation phenomena in tubes carrying fluid', AMSE Journal of Applied Mechanics 39, 1980, 213-230.
13. Bajaj, A. K. and Sethna, P. R., 'Bifurcations in three dimensional motions of articulated tubes: Part 2, Nonlinear analysis', ASME Journal of Applied Mechanics 49, 1982, 612-618.
14. Bajaj, A. K. and Sethna, P. R., 'Flow induced bifurcations in three dimensional oscillatory motions of continuous tubes', AMSE Journal of Applied Mechanics 44, 1984, 270-286.
15. Thompson, J. M. T. and Lunn, T. S., 'Static elastica formulations of a pipe conveying fluid', Journal of Sound and Vibration 77, 1981, 127-132.
16. Sri Namachchivaya, N. and Tien, W. M., 'Bifurcation behaviour of nonlinear pipes conveying pulsating flow', Journal of Fluid and Structures 3, 1989, 609-629.
17. Yoshizawa, M., Nao, H., Hasegawa, E., and Tsujioka, Y., 'Lateral vibration of a flexible pipe conveying fluid with pulsating flow', Bulletin of JSME 29, 1986, 2249-2250.
18. Paidoussis, M. P. and Li, 'Pipes conveying fluid: A model dynamical problem', Journal of Fluid and Structures 7, 1993, 137-204.
19. Tang, D. M. and Dowell, E. H., 'On the threshold force for chaotic motions for a forced buckled beam', ASME Journal of Applied Mechanics 55, 1988, 190-196.
20. Paidoussis, M. P. and Moon, F. C., 'Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid', in Nonlinear Interaction Effects and Chaotic Motions, Proceedings International Symposium on Flow Induced Vibration and Noise (ASME), M. M. Reischman, M. P. Paidoussis, and R. J. Hansen (eds.), 1988, pp. 107-133.
21. Paidoussis, M. P. and Moon, F. C., 'Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid', Journal of Fluids and Structures 3, 1988, 567-591.
22. Dowell, E. H. and Pezeshki, C., 'On the understanding of chaos in Duffing's equation including a comparison with experiment', ASME Journal of Applied Mechanics 53 1986, 5-9.
23. Moon, F. C., Chaotic Vibrations, John Wiley & Sons, New York.
24. Grebogi, C., Ott, E., and Yorke, J. A., 'Fractal basin boundaries, long lived chaotic transients and unstable-unstable pair bifurcation', Physics Review Letters 50(13), 1983, 935-938.
25. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, John Wiley, New York, 1979.
26. Zavodney, L. D. and Nayfeh, A. H., The response of single degree of freedom system with quadratic and cubic nonlinearities to a fundamental parametric resonance', Journal of Sound and Vibration 120(1), 1988, 63-93.