Chaotic Motions of a Constrained Pipe Conveying Fluid: Comparison Between Simulation, Analysis, and Experiment

[+] Author and Article Information
M. P. Paidoussis, G. X. Li

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

R. H. Rand

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

J. Appl. Mech 58(2), 559-565 (Jun 01, 1991) (7 pages) doi:10.1115/1.2897220 History: Received November 21, 1989; Revised October 02, 1990; Online March 31, 2008


A refined analytical model is presented for the dynamics of a cantilevered pipe conveying fluid and constrained by motion limiting restraints. Calculations with the discretized form of this model with a progressively increasing number of degrees of freedom, N , show that convergence is achieved with N = 4 or 5, which agrees with previously performed fractal dimension calculations of experimental data. Theory shows that, beyond the Hopf bifurcation, as the flow is increased, a pitchfork bifurcation is followed by a cascade of period doubling bifurcations leading to chaos, which is in qualitative agreement with observation. The numerically computed theoretical critical flow velocities are in excellent quantitative agreement (5–10 percent) with experimental values for the thresholds of the Hopf and period doubling bifurcations and for the onset of chaos. An approximation for the critical flow velocity for the loss of stability of the post-Hopf limit cycle is also obtained by using center manifold concepts and normal form techniques for a simplified version of the analytical model; it is found that the values obtained in this manner are approximately within 10 percent of those computed numerically.

Copyright © 1991 by The American Society of Mechanical Engineers
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