Low-dimensional chaos in a flexible tube conveying fluid

This paper describes the observed dynamical behavior of a cantilevered pipe conveying fluid, an autonomous nonconservative (circulatory) dynamical system, limitcycle 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.