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RESEARCH PAPERS

Low-Dimensional Chaos in a Flexible Tube Conveying Fluid

[+] Author and Article Information
M. P. Païdoussis

Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canada

J. P. Cusumano

Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802

G. S. Copeland

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853

J. Appl. Mech 59(1), 196-205 (Mar 01, 1992) (10 pages) doi:10.1115/1.2899428 History: Received August 02, 1989; Revised May 03, 1991; Online March 31, 2008

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, Poincaré 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.

Copyright © 1992 by The American Society of Mechanical Engineers
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