Skip to main content
SpringerLink
Log in

Some simple mechanical systems with a post-buckling path bifurcating at infinity

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

It is shown, that simple structures composed of rigid bodies exist, which possess an equilibrium position, that is stable for all finite loadings, and a post-buckling path bifurcating off for the loading at infinity. This property only occurs for the perfect system as imperfect systems have a finite critical loading. Methods of singularity theory are applied to investigate this type of bifurcation. In simple cases it is possible to give the full (versal) unfolding by means of catastrophe theory. But for higher dimensional cases especially adapted concepts are considered to be the proper mean, particularly as common reduction principles do not work for this type of bifurcation. To show that bifurcation at infinity does not only occur for static, problems a reference to an example from hydrodynamics is given.

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. La Salle, J., Lefschetz, S.: Stability by Liapunov's direct method with applications. New York: Academic Press 1961.

    Google Scholar 

  2. Iooss, G., Joseph, D. D.: Elementary stability and bifurcation theory. New York-Heidelberg-Berlin: Springer 1980.

    Google Scholar 

  3. Chow, S. N., Hale, J.: Methods of bifurcation theory. New York-Heidelberg-Berlin: Springer 1982.

    Google Scholar 

  4. Poston, T., Stewart, I.: Catastrophe theory and its applications. London: Pitman 1978.

    Google Scholar 

  5. Gilmore, R.: Catastrophe theory for scientists, and engineers. John Wiley 1981.

  6. Hale, J. K.: Restricted generic bifurcation, nonlinear analysis, p. 83–98, New York: Academic Press 1978.

    Google Scholar 

  7. Golubitsky, M., Schaeffer, D.: A theory of imperfect bifurcation via singularity theory Comm. Pure Appl. Math.23, 21–98 (1979).

    Google Scholar 

  8. Joseph, D. D.: Stability of fluid motions, Springer Tracts in Natural Philosophy, Vol.27, Berlin-Heidelberg-New York: Springer 1976.

    Google Scholar 

  9. Drazin, P. G., Reid, W. H.: Hydrodynamic stability. London-New York-New Rochelle-Melbourne-Sydney: Cambridge University Press 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mechanik Technische Universität Wien, Karlsplatz 13, A-1040, Wien, Austria

    R. Scheidl

Authors
  1. R. Scheidl
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 9 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scheidl, R. Some simple mechanical systems with a post-buckling path bifurcating at infinity. Acta Mechanica 59, 1–10 (1986). https://doi.org/10.1007/BF01177056

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01177056

Keywords

Search

Navigation