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

First Page Preview

View Large
First page PDF preview
Copyright © 2003 by ASME
Topics: Collapse , Cylinders , Whirls
Your Session has timed out. Please sign back in to continue.


Tucker,  R. W., and Wang,  C., 1999, “An Integrated Model for Drill-String Dynamics,” J. Sound Vib., 224, pp. 123–165.
Huang,  N. C., and Pattillo,  P. D., 2000, “Helical Buckling of a Tube in an Inclined Wellbore,” Int. J. Non-Linear Mech., 35, pp. 911–923.
Fraser,  W. B., 1993, “On the Dynamics of the Two-for-One Twister,” Proc. R. Soc. London, Ser. A, 447, pp. 409–425.
van der Heijden,  G. H. M., 2001, “The Static Deformation of a Twisted Elastic Rod Constrained to Lie on a Cylinder,” Proc. R. Soc. London, Ser. A, 457, pp. 695–715.
Fraser,  W. B., and Stump,  D. M., 1998, “The Equilibrium of the Convergence Point in Two-Strand Yarn Plying,” Int. J. Solids Struct., 35, pp. 285–298.
Coleman,  B. D., and Swigon,  D., 2000, “Theory of Supercoiled Elastic Rings With Self-Contact and Its Application to DNA Plasmids,” J. Elast., 60, pp. 173–221.
Stump,  D. M., Fraser,  W. B., and Gates,  K. E., 1998, “The Writhing of Circular Cross-Section Rods: Undersea Cables to DNA Supercoils,” Proc. R. Soc. London, Ser. A, 454, pp. 2123–2156.
Stump,  D. M., and Fraser,  W. B., 2000, “Multiple Solutions for Writhed Rods: Implications for DNA Supercoiling,” Proc. R. Soc. London, Ser. A, 456, pp. 455–467.
Clark,  J. D., Fraser,  W. B., and Stump,  D. M., 2001, “Modelling of Tension in Yarn Package Unwinding,” J. Eng. Math., 40, pp. 59–75.
Jansen,  J. D., 1991, “Non-Linear Rotor Dynamics as Applied to Oilwell Drillstring Vibrations,” J. Sound Vib., 147, 115–135.
van der Heijden,  G. H. M., and Thompson,  J. M. T., 2000, “Helical and Localised Buckling in Twisted Rods: A Unified Analysis of the Symmetric Case,” Nonlinear Dyn., 21, pp. 71–99.
Holmes,  P., Domokos,  G., Schmitt,  J., and Szeberényi,  I., 1999, “Constrained Euler Buckling: An Interplay of Computation and Analysis,” Comput. Methods Appl. Mech. Eng., 170, pp. 175–207.
van der Heijden,  G. H. M., Champneys,  A. R., and Thompson,  J. M. T., 2002, “Spatially Complex Localisation in Twisted Elastic Rods Constrained to a Cylinder,” Int. J. Solids Struct., 39, pp. 1863–1883.
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.


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.)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In