Low-dimensional chaos in a flexible tube conveying fluid

M. P. Paidoussis, Joseph Paul Cusumano, G. S. Copeland

Research output: Contribution to journalConference article

Abstract

This paper describes the observed dynamical behavior of a cantilevered pipe conveying fluid, an autonomous nonconservative (circulatory) dynamical system, limit-cycle motions of which, upon loss of stability via a Hopf bifurcation, interact with nonlinear motion-limiting constraints. This system was found to become chaotic at sufficiently high flow rates. Motions of the system, sensed by an optical tracking system, were analyzed by Fast Fourier Transform, autocorrelation, Polncare map, and delay embedding techniques, and the fractal dimension of the system, dc, was calculated. Values of dc = 1.03, 1.53, and 3.20 were obtained in the period-1, 'fuzzy' period-2 and chaotic regimes of oscillation of the system. Based on these calculations, a four-dimensional analytical model was constructed, which was found to capture the essential dynamical features of observed behavior quite well.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalAmerican Society of Mechanical Engineers (Paper)
StatePublished - Dec 1 1991

Fingerprint

Hopf bifurcation
Conveying
Fractal dimension
Autocorrelation
Chaos theory
Fast Fourier transforms
Analytical models
Dynamical systems
Pipe
Flow rate
Fluids

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

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abstract = "This paper describes the observed dynamical behavior of a cantilevered pipe conveying fluid, an autonomous nonconservative (circulatory) dynamical system, limit-cycle motions of which, upon loss of stability via a Hopf bifurcation, interact with nonlinear motion-limiting constraints. This system was found to become chaotic at sufficiently high flow rates. Motions of the system, sensed by an optical tracking system, were analyzed by Fast Fourier Transform, autocorrelation, Polncare map, and delay embedding techniques, and the fractal dimension of the system, dc, was calculated. Values of dc = 1.03, 1.53, and 3.20 were obtained in the period-1, 'fuzzy' period-2 and chaotic regimes of oscillation of the system. Based on these calculations, a four-dimensional analytical model was constructed, which was found to capture the essential dynamical features of observed behavior quite well.",
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Low-dimensional chaos in a flexible tube conveying fluid. / Paidoussis, M. P.; Cusumano, Joseph Paul; Copeland, G. S.

In: American Society of Mechanical Engineers (Paper), 01.12.1991, p. 1-10.

Research output: Contribution to journalConference article

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AU - Paidoussis, M. P.

AU - Cusumano, Joseph Paul

AU - Copeland, G. S.

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