Skip to main content
SpringerLink
Log in

Post-critical behaviour of a uniform cantilever column subjected to a tip concentrated subtangential follower force with small damping

  • Published:
Forschung im Ingenieurwesen A Aims and scope Submit manuscript

Abstract

Large deflection analysis of a uniform cantilever column under a tip concentrated subtangential follower force has been studied using the dynamic criterion. The problem is solved with a simple and reliable iterative numerical scheme. The eigencurve, post-critical load and corresponding coalescence frequency parameter wherever applicable for different values of the subtangential parameter and the tip angle of the column are presented. The post-critical loads are also determined by considering arbitrarily (vanishingly) small internal damping forces. It is noted that small damping has a destabilizing effect.

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

Literature

  1. Beck, M.: Die Knicklast des einseitig eingespannenten, tangential gedrückten Stabes. ZAMP Vol. 3 (1952) pp. 225/28.

    Article  MATH  Google Scholar 

  2. Ziegler, H.: Linear Elastic Stability. ZAMP Vol. 4 (1953) pp. 89/184.

    Article  MathSciNet  MATH  Google Scholar 

  3. Dejneko, K.S., aM.J. Leonov: The dynamic method of investigating the stability of a bar in compression. PMM Vol. 19 (1955) pp. 738/44.

    MATH  Google Scholar 

  4. Ziegler, H.: On the concept of elastic stability. Advances in Appl. Mech. Vol. 4 (1956) pp. 351/403.

    MathSciNet  Google Scholar 

  5. Timoshenko, S.P., a.J.M. Gere: Theory of Elastic Stability. New York: McGraw-Hill 1961.

    Google Scholar 

  6. Leipholz, H.: Anwendung des Galerkinschen Verfahrens auf nichtkonservative Stabilitätsprobleme des elastischen Stabes. ZAMP Vol. 13 (1962) pp. 359/72.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bolotin, V.V.: Nonconservative problems of the theory of elastic stability. London: Pergamon Press 1963.

    MATH  Google Scholar 

  8. Bolotin, V.V.: Dynamic stability of elastic systems. San Francisco: Holden-Day 1964.

    MATH  Google Scholar 

  9. Herrmann, G., a.R.W. Bungay: On the stability of elastic systems subjected to nonconservative forces. J. Appl. Mech. Vol. 31 (1964) pp. 435/40.

    MathSciNet  Google Scholar 

  10. Herrmann, G.: Stability of equilibrium of elastic systems subjected to nonconservative forces. Appl. Mech. Rev. Vol. 20 (1967) pp. 103/08.

    MathSciNet  Google Scholar 

  11. Ziegler, H.: Principles of Structural Stability. Waltham, MA: Blaisdell, 1968.

    Google Scholar 

  12. Leipholz, H.: Stability Theory. New York: Academic Press 1970.

    MATH  Google Scholar 

  13. Barsoum, R.S.: Finite element method applied to the problem of stability of a nonconservative system. Int. J. Num. Meth. Engng. Vol. 3 (1971) pp. 63/87.

    Article  MATH  Google Scholar 

  14. Kikuchi, F.: A finite element method for non-self adjoint problems. Int. J. Num. Meth. Engng. Vol. 6 (1973) pp. 39/54.

    Article  MathSciNet  MATH  Google Scholar 

  15. Venkateswara Rao, G., a.R.V. Narasimha Rao: Galerkin finite element solution for the stability of cantilever columns subjected to a tangential loads. AIAA J. Vol. 13 (1973) pp. 690/91.

    Google Scholar 

  16. Celep, Z.: On the lateral stability and eigencurves of elastic beams subjected to vertical and follower forces. Acta Mech. Vol. 25 (1977) pp. 257/65.

    Article  MATH  Google Scholar 

  17. Leipholz, H.H.E. a.T. Polzin: On a lower bound theorem for the buckling load of elastic beams subjected to nonconservative compressive follower loads. Acta Mech. Vol. 25 (1977) pp. 171/86.

    Article  MathSciNet  MATH  Google Scholar 

  18. Atanachovic, T.M., a.B.M. Milisavljecic: Some estimates for a buckling problem. Acta Mech. Vol. 41 (1981) pp. 63/71.

    Article  MathSciNet  Google Scholar 

  19. Nemat-Nasser, S., S. Prasad a.G. Herrmann: Destabilizing effect of velocity dependent forces in nonconservative continuous systems. AIAA Journal Vol. 4 (1966) pp. 1276/80.

    Google Scholar 

  20. Bolotin, V.V., a.N.I. Zhinzher: Effects of damping on stability of elastic systems subjected to nonconservative forces. Int. J. Solids and Structures Vol. 5 (1969) pp. 965/89.

    Article  MATH  Google Scholar 

  21. Shieh, R. C.: Dynamic instability of a cantilever column subjected to a follower force including thermoelastic coupling. J. Appl. Mech. Vol. 38 (1971) pp. 839/46.

    MATH  Google Scholar 

  22. Anderson, G.L.: Determination of some critical flutter loads in the presence of arbitrarily small velocity dependent forces. J. Sound and Vibration Vol. 41 (1975) pp. 143/53.

    Article  MATH  Google Scholar 

  23. Budiansky, B.: Theory of buckling and post-buckling behaviour of elastic structures. Advances in Appl. Mech. Vol. 14 (1974) pp. 1/65.

    Article  Google Scholar 

  24. Plaut, R.A.: Post-buckling analysis of nonconservative elastic systems. J. Struct. Mech. Vol. 4 (1976) pp. 395/416.

    Google Scholar 

  25. ElNaschie, M.S.: Post-critical behaviour of the Beck problem. J. Sound and Vibration. Vol. 48 (1976) pp. 341/44.

    Article  Google Scholar 

  26. Venkateswara Rao, G., aP.C. Raju: Post-buckling of uniform cartilever columns—Galerkin finite element solution. Engineering Fracture Mech. Vol. 9 (1977) pp. 1/4.

    Article  Google Scholar 

  27. Plaut, R.A.: Post-buckling analysis of continuous non-conservative elastic systems. Acta Mech. Vol. 30 (1978) pp. 51/64.

    Article  MathSciNet  MATH  Google Scholar 

  28. Nageswara Rao, B., a.G. Venkateswara Rao: Post-buckling analysis of a uniform cantilever column subjected to a tip concentrated subtangential follower force. Forsch. Ing.-Wes. Vol. 55 (1989) No. 2, pp. 36/38.

    Article  Google Scholar 

  29. Nageswara Rao, B., a.G. Venkateswara Rao: Large Deflections of a Cantilever Beam Subjected to a Rotational Distributed Loading. Forsch. Ing.-Wes. Vol. 55 (1989) No. 4, pp. 116/20.

    Google Scholar 

  30. Wagner, H.: Larger—amplitude free vibrations of a beam. J. Appl. Mech. Vol. 32 (1965) pp. 887/92.

    Google Scholar 

  31. Nageswara Rao, B., aG. Venkateswara Rao: Stability of Tapered Cantilever Columns Subjected to a Tip Concentrated Subtangential Follower Force. Forsch. Ing.-Wes. Vol. 56 (1990) No. 3, pp. 93/96.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Structural Design and Analysis Division, Structural Engineering Group, Vikram Sarabhai Space Centre, Trivandrum, India

    B. Nageswara Rao & G. Venkateswara Rao

Authors
  1. B. Nageswara Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Venkateswara Rao
    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

Nageswara Rao, B., Venkateswara Rao, G. Post-critical behaviour of a uniform cantilever column subjected to a tip concentrated subtangential follower force with small damping. Forsch Ing-Wes 57, 81–86 (1991). https://doi.org/10.1007/BF02561170

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02561170

Keywords

Search

Navigation