Low-dimensional chaos in a flexible tube conveying fluid

M. P. Paidoussis; J. P. Cusumano; G. S. Copeland

Low-dimensional chaos in a flexible tube conveying fluid

M. P. Paidoussis, J. P. Cusumano, G. S. Copeland

Research output: Contribution to journal › Conference article › peer-review

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, d_c, was calculated. Values of d_c = 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 language	English (US)
Pages (from-to)	1-10
Number of pages	10
Journal	American Society of Mechanical Engineers (Paper)
State	Published - Dec 1 1991
Event	ASME Winter Annual Meeting - Atlanta, GA, USA Duration: Dec 1 1991 → Dec 6 1991

All Science Journal Classification (ASJC) codes

Mechanical Engineering

Cite this

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title = "Low-dimensional chaos in a flexible tube conveying fluid",

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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T1 - Low-dimensional chaos in a flexible tube conveying fluid

AU - Paidoussis, M. P.

AU - Cusumano, J. P.

AU - Copeland, G. S.

PY - 1991/12/1

Y1 - 1991/12/1

N2 - 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.

AB - 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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M3 - Conference article

AN - SCOPUS:0026387114

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T2 - ASME Winter Annual Meeting

Y2 - 1 December 1991 through 6 December 1991

ER -

Low-dimensional chaos in a flexible tube conveying fluid

Abstract

All Science Journal Classification (ASJC) codes

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