Abstract
In this paper we investigate the nonlinear dynamics of a cantilever elastic pipe that contains pulsatile flow. The equation of motion was derived by using Hamiltonian action function. We use Galerkin's technique to include only finite number of spatial modes in the solution.
The stability chart of the time-varying system was computed in the space of the relative perturbation amplitude of the flow velocity and dimensionless forcing frequency using an efficient numerical method based on Chebyshev polynomials. In the near of some critical regions bifurcation diagrams were also computed which show secondary Hopf bifurcations and phase locking followed by chaotic motion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ashley, H. and Haviland, G., ‘Bending vibrations of a pipeline containing flowing fluid’, J. Appl. Mech. 17 (1950) 229-232.
Bautin, N.N., The Behaviour of Dynamical Systems Near to the Boundary of Their Stability Domains, Gostechizdat, Moscow, 1948 (in Russian).
Blevins, R.D., Flow-induced Vibration, Van Nonstrand Reinhold, New York, 1990.
Farkas, M., Periodic Motions, Springer-Verlag, New York, 1994.
Hopf, E., ‘Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems’, Ber. Verh. Sachs. Akad. Wiss., Leipzig, Math.-Nat. 95 (1942) 3-22.
Liapunov, A.M., Problème Générale de la Stabilité de Mouvement, Annals of Mathematics Studies 17, Princeton, NJ, 1947 (originally: Kharkov, 1892, in Russian).
Marsden, J.E. and McCracken, M., The Hopf Bifurcation and its Applications, Springer-Verlag, New York, 1976.
Païdoussis, M.P. and Issid, N.T., ‘Dynamic stability of pipes conveying fluid’, J. Sound Vib. 33(3) (1974) 267-294.
Païdoussis, M.P. and Issid, N.T., ‘Experiments on parametric resonance of pipes containing pulsatile flow’, J. Appl. Mech. 98(2) (1976) 198-202.
Pandiyan, R. and Sinha, S.C., ‘Analysis of time-periodic nonlinear dynamical systems undergoing bifurcations’, Nonlinear Dyn. 8 (1995) 21-43.
Païdoussis, M.P. and Li, G.X., ‘Pipes conveying fluid: a model dynamical problem’, J. Fluids Struct. 7 (1993) 137-204.
Semler, C., Li, G.X. and Païdoussis, M.P., ‘The non-linear equations of motion of pipes conveying fluid’, J. Sound Vib. 169(5) (1994) 577-599.
Sinha, S.C. and Wu, D.-H., ‘An efficient computational scheme for the analysis of periodic system’, J. Sound Vib. 151 (1991) 91-117.
Troger, H., Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists, Springer-Verlag, Wien, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szabó, Z. Nonlinear Analysis of a Cantilever Pipe Containing Pulsatile Flow. Meccanica 38, 163–174 (2003). https://doi.org/10.1023/A:1022039905834
Issue Date:
DOI: https://doi.org/10.1023/A:1022039905834