Skip to main content
SpringerLink
Log in

Stability of an extensible rotating rod

  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

The stability of a rotating, linearly elastic, extensibte rod against deflection is analysed. It is shown that the critical rotation speed is determined by the lowest eigenvalue of the linearized equations of equilibrium. The critical speed turns out to be independent of the extensibility of the rod. Load and shape imperfections change the form of the bifurcation diagram, they generate a universal unfolding of the bifurcation of the perfect rod. The numerical calculation of the deflection of the perfect rod show that the extensibility of the rod tends to increase the deflection.

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. Odeh, F.; Tadjabakhsh, I.: A nonlinear eigenvalue problem for rotating rods. Arch. Ration. Mech. Anal. 20 (1965) 81–94

    Google Scholar 

  2. Bazely, N.; Zwahlen, B. Remarks on the bifurcation solutions of a nonlinear eigenvalue problem. Arch. Ration. Mech. Anal. 28 (1968) 51–58

    Google Scholar 

  3. Wang, C.-Y.: On the bifurcation solution of an axially rotating rod. Quart. J. Mech. Appl. Math. 35 (1982) 391–402

    Google Scholar 

  4. Atanacković, T. M.: Estimates of maximum deflection for a rotating rod. Quart. J. Mech. Appl. Math, 37 (1984) 515–523

    Google Scholar 

  5. Atanacković, T. M.: Buckling of rotating compressed rods. Acta Mech. 60 (1986) 49–66

    Google Scholar 

  6. Atanacković, T. M.: Stability of rotating compressed rod with imperfections. Math. Proc. Camb. Phil. Soc. 101 (1987) 593–607

    Google Scholar 

  7. Pflügler A. Stabilitätsprobleme der Elastostatik. Berlin: Springer 1975

    Google Scholar 

  8. Antman, S.: General solutions for plane extensible easticae having nonlinear stressstrain laws. Quart. Appl. Math. 26 (1968) 35–47

    Google Scholar 

  9. Gilmore, R. Catastrophe theory for scientists and engineers. New York: Wiley-Interscience 1981

    Google Scholar 

  10. Vladimirov, V. S.: Generalized functions in mathematical physics. Moscow: Mir 1979

    Google Scholar 

  11. Chow, S.-N.; Hale, J. K.: Methods of bifurcation theory. New York: Springer 1982

    Google Scholar 

  12. Golubitsky, M.; Schaeffer, D. G.: Singularities and groups in bifurcation theory. Vol. 1. New York: Springer 1985

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultet tehničkih nauka, Veljka Vlahovića 3, 21000, NOVISAD, Yugoslavia

    T. Atanacković

  2. Hermann-Föttinger-Institut, Technische Universität Berlin, D-1000, Berlin 12

    M. Achenbach

Authors
  1. T. Atanacković
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Achenbach
    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

Atanacković, T., Achenbach, M. Stability of an extensible rotating rod. Continuum Mech. Thermodyn 1, 81–95 (1989). https://doi.org/10.1007/BF01141995

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01141995

Keywords

Search

Navigation