Skip to main content
SpringerLink
Log in

On the interaction of solitary waves of flexure in elastic rods

  • Original Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

A numerical study is made to determine whether the partial differential equations governing planar, twist-free motions in a theory of the dynamics of elastic rods are completely integrable in the sense of soliton theory. The theory in which the equations arise is due to Kirchhoff and Clebsch and is complete to within an error of order two in an appropriate dimensionless measure of thickness and strain. A recently developed energy-preserving finite-difference scheme is employed to determine the consequences of the interaction of solitary traveling waves, which, in the present twist-free case, are loops traveling at constant speed. It is found that the change induced in such a loop-wave upon collision with another is more than a shift in phase.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Caflisch, R. E., Maddocks, J. H.: Nonlinear dynamical theory of the elastica. Proc. R. Soc. Edinburgh99A, 1–23 (1984).

    Google Scholar 

  2. Coleman, B. D., Dill, E. H.: Flexure waves in elastic rods. J. Acoust. Soc. Am.91, 2663–2673 (1992).

    Google Scholar 

  3. Falk, R. S., Xu, J.-M.: Convergence of a second-order scheme for the nonlinear dynamical equations of elastic rods. SIAM J. Numer. Anal. (in press).

  4. Xu, J.-M.: An analysis of the dynamical equations of elastic rods and their numerical approximation. Doctoral Dissertation, Rutgers University, New Brunswick 1992.

    Google Scholar 

  5. Dichmann, D. J., Maddocks, J. H., Pego, R. L.: Hamiltonian dynamics of an elastica and the stability of solitary waves; preprint.

  6. Maddocks, J. H., Dichmann, D. J.: Conservation laws in the dynamics of rods. J. Elasticity34, 83–96 (1994).

    Google Scholar 

  7. Coleman, B. D., Dill, E. H., Lembo, M., Lu, Z., Tobias, I.: On the dynamics of rods in the theory Kirchhoff and Clebsch. Arch. Rational Mech. Anal.121, 339–359 (1993).

    Google Scholar 

Download references

Author information

Author notes

  1. B. D. Coleman & J. -M. Xu

    Present address: Program in Mechanics, Rutgers University, P.O. Box 909, 08854, Piscataway, NJ, USA

Authors and Affiliations

    Authors
    1. B. D. Coleman
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. J. -M. Xu
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Coleman, B.D., Xu, J.M. On the interaction of solitary waves of flexure in elastic rods. Acta Mechanica 110, 173–182 (1995). https://doi.org/10.1007/BF01215423

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01215423

    Keywords

    Search

    Navigation