Limit-cycle oscillations of a heavy whirling cable subject to aerodynamic drag

James David Clark, Wynstone Barrie Fraser, Christopher D. Rahn, Arun Rajamani

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper a simple experimental system consisting of a length of cable, fixed to the edge of a rotating disc at its upper end, and free at its lower end or with a point mass (drogue) attached there, is described. This system exhibits a rich variety of bifurcation behaviours as the length of cable, angular speed of the fixed end, mass of the drogue and elasticity of the cable is varied. Bifurcation diagrams for the quasistationary configurations (cable shapes that appear stationary with respect to the rotating reference frame) are described. Linearized stability analyses of these quasistationary balloons are compared with solutions to the full time-dependent equations of motion. It is shown that there is an exchange of stability at the turning points of the quasi-stationary bifurcation curves, and that Hopf bifurcations occur at otherwise undistinguished points of these curves. It is shown that limit-cycle oscillations of the system occur at angular speeds corresponding to points on the bifurcations curves in the neighbourhood of the Hopf bifurcation points. These oscillations have been observed experimentally.

Original languageEnglish (US)
Pages (from-to)875-893
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2055
DOIs
StatePublished - Mar 8 2005

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aerodynamic drag
Aerodynamic drag
Drag
Cable
Aerodynamics
Limit Cycle
cables
Cables
Oscillation
Angular speed
Bifurcation Curve
oscillations
cycles
Hopf bifurcation
Bifurcation (mathematics)
Hopf Bifurcation
curves
Rotating Disk
Balloon
Balloons

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

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abstract = "In this paper a simple experimental system consisting of a length of cable, fixed to the edge of a rotating disc at its upper end, and free at its lower end or with a point mass (drogue) attached there, is described. This system exhibits a rich variety of bifurcation behaviours as the length of cable, angular speed of the fixed end, mass of the drogue and elasticity of the cable is varied. Bifurcation diagrams for the quasistationary configurations (cable shapes that appear stationary with respect to the rotating reference frame) are described. Linearized stability analyses of these quasistationary balloons are compared with solutions to the full time-dependent equations of motion. It is shown that there is an exchange of stability at the turning points of the quasi-stationary bifurcation curves, and that Hopf bifurcations occur at otherwise undistinguished points of these curves. It is shown that limit-cycle oscillations of the system occur at angular speeds corresponding to points on the bifurcations curves in the neighbourhood of the Hopf bifurcation points. These oscillations have been observed experimentally.",
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Limit-cycle oscillations of a heavy whirling cable subject to aerodynamic drag. / Clark, James David; Fraser, Wynstone Barrie; Rahn, Christopher D.; Rajamani, Arun.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, No. 2055, 08.03.2005, p. 875-893.

Research output: Contribution to journalArticle

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