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BRIEF NOTES

Helical Collapse of a Whirling Elastic Rod Forced to Lie on a Cylinder

[+] Author and Article Information
G. H. M. van der Heijden

Center for Nonlinear Dynamics, University College London, London WC1E 6BT, UK  

W. B. Fraser

School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia

J. Appl. Mech 70(5), 771-774 (Oct 10, 2003) (4 pages) doi:10.1115/1.1604833 History: Received January 02, 2001; Revised May 06, 2003; Online October 10, 2003

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Copyright © 2003 by ASME
Topics: Collapse , Cylinders , Whirls
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References

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Thompson,  J. M. T., van der Heijden,  G. H. M., and Neukirch,  S., 2002, “Supercoiling of DNA Plasmids: Mechanics of the Generalized Ply,” Proc. R. Soc. London, Ser. A, 458, pp. 959–985.

Figures

Grahic Jump Location
Phase-plane diagrams for the equivalent oscillator (16) subject to (19) for r=1,K=0.8 and (a) P=Pc=0.1683, (b) P=0.1322. Notice the saddle connection between the origin and the nontrivial fixed point at ϕ=0.4660 (26.70°) in (a).
Grahic Jump Location
Load-deflection characteristic and evolution, under varying load P, of the localized solution with initial ϕ>0. There is a critical collapse load corresponding to a right-handed tensile helix at Pc=0.1683. The triangle indicates where the rod starts to go backwards on the cylinder over some section of rod. This is soon followed by self-intersection, so the dashed part of the curve, including the second critical load at P=0.5123, is nonphysical. D is the dimensionless end shortening. (r=1,K=0.8.)

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