Helical collapse of a whirling elastic rod forced to lie on a cylinder

G.H.M. van der Heijden & W.B. Fraser

Extending our previous work, we apply the large-deflection rod theory to a periodically driven elastic rod in continuous contact with a cylindrical surface. Applications of this problem are found in oilwell drilling and textile yarn spinning. The previously uncovered quasi-statical helical collapse of the constrained rod is studied in the quasi-stationary context, and its occurrence examined as a function of the applied end loads and the driving frequency. Balanced plies, which are also relevant in DNA supercoiling, are shown to be special solutions of the problem under consideration.

keywords: whirling elastic rod, quasi-stationary solutions, constraining cylinder, helical collapse, loaded ply

J. Appl. Mech. 70, 771-774 (2003)