Skip to main content

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 52))

  • 302 Accesses

Abstract

In this paper we study localised buckling in elastic rods with non-symmetric crosssection, which has applications in undersea cable and drillstring buckling as well as in DNA engineering [10]. Strong evidence will be given of the existence of an infinity of localised buckling modes. In addition, we show how these solutions can be computed numerically, and how some structure can be found in their multitude.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belyakov, L.A., Šil’nikov, L.P., Homoclinic curves and complex solitary waves, Selecta Mathematica Sovietica 9, 219–228 (1990).

    Google Scholar 

  2. Champneys, A.R., Spence, A., Hunting for homoclinic orbits: a shooting technique, Adv. Comp. Math. 1, 81–108 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  3. Champneys, A.R. & Thompson, J.M.T., A multiplicity of localised buckling modes for twisted rod equations, to appear (1996).

    Google Scholar 

  4. Coyne, J., Analysis of the formation and elimination of loops in twisted cable, IEEE J. Ocean. Eng. 15, 72–83 (1990).

    Article  Google Scholar 

  5. Devaney, R.L., Homoclinic orbits in Hamiltonian systems, J. Diff. Eqns. 21, 431–438 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  6. Doedel, E.J. & Kernévez, J.P., AUTO: Software for continuation and bifurcation problems in ordinary differential equations, Applied Mathematics Report, California Institute of Technology (1986).

    Google Scholar 

  7. Heijden, G.H.M. van der, Champneys, A.R., Thompson, J.M.T., Load-deflection characteristics of localised torsional buckling modes in rods with non-circular cross-section, to be submitted.

    Google Scholar 

  8. Iooss, G. & Pérouème, M.C., Perturbed homoclinic solutions in reversible 1:1 resonance vector fields, J. Diff. Eqns. 102, 62–88 (1993).

    Article  MATH  Google Scholar 

  9. Love, A.E.H., A treatise on the mathematical theory of elasticity, 4th ed. (Cambridge University Press, Cambridge, 1927).

    MATH  Google Scholar 

  10. Thompson, J.M.T. & Champneys, A.R., From helix to localized writhing in the torsional post-buckling of elastic rods, Proc. R. Soc. Lond. A452, 117–138 (1996).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Van Der Heijden, G.H.M., Champneys, A.R., Thompson, J.M.T. (1997). Homoclinic Bifurcation and Localised Torsional Buckling of Elastic Rods. In: Van Campen, D.H. (eds) IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems. Solid Mechanics and Its Applications, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5778-0_18

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5778-0_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6439-2

  • Online ISBN: 978-94-011-5778-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics