Advertisement

Columns with Damping

  • Yoshihiko SugiyamaEmail author
  • Mikael A. Langthjem
  • Kazuo Katayama
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 255)

Abstract

Ziegler discovered in 1952 that the introduction of damping in an elastic system under a follower force may have a destabilizing effect [1]. This caused a great deal of interest among structural dynamists, interest that has continued to date [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. This chapter discusses the effect of internal damping on the flutter limit of a cantilevered column under a follower force. In place of Beck’s column, we consider Pflüger’s column, which has a tip mass [7, 8]. This chapter deals with a Pflüger’s column with internal (Kelvin-Voigt type) and external damping.

References

  1. 1.
    Ziegler, H. (1952). Die Stabilitätkrierien der Elastomechanik. Ingenieur-Archiv, 20, 49–56.CrossRefGoogle Scholar
  2. 2.
    Herrmann, G., & Jong, I.-C. (1965). On the destabilizing effect of damping in nonconservative elastic systems. Journal of Applied Mechanics, 32(3), 592–597.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ziegler, H. (1968). Principles of structural stability. Waltham: Blaisdell Publishing Co.Google Scholar
  4. 4.
    Bolotin, V. V., & Zhinzher, N. J. (1969). Effects of damping on stability of elastic systems subjected to nonconservative forces. International Journal of Solid and Structures, 5, 965–989.CrossRefGoogle Scholar
  5. 5.
    Kirillov, O. N., & Seyranian, A. P. (2005). The effect of small internal and external damping on the stability of distributed nonconservative systems. Journal of Applied Mathematics and Mechanics, 69(4), 529–552.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Tommasini, M., Kirillov, O. N., Misseroni, D., & Bigoni, D. (2016). The destabilizing effect of external damping: Singular flutter boundary for the Pflüger column with vanishing external dissipation. Journal of the Mechanics and Physics of Solids, 91, 204–215.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Pflüger, A. (1955). Zur Stabilität des tangential gedrückten Stabes. Zeitschrift für Angewandte Mathematik und Mechanik, 51(4), 191.CrossRefGoogle Scholar
  8. 8.
    Sugiyama, Y., Kashima, K., & Kawagoe, H. (1976). On an unduly simplified model in the non-conservative problems of elastic stability. Journal of Sound and Vibration, 45(2), 237–247.CrossRefGoogle Scholar
  9. 9.
    Pedersen, P. (1984). Sensitivity analysis for non-self-adjoint systems. In Komkov, V. (Ed.), Sensitivity of Functionals with Applications to Engineering Sciences (pp. 119–130). Berlin: Springer.Google Scholar
  10. 10.
    Ryu, S.-U., & Sugiyama, Y. (2003). Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force. Computers & Structures, 81, 265–271.CrossRefGoogle Scholar
  11. 11.
    Fawzy, I., & Bishop, R. E. D. (1976). On the dynamics of linear nonconservative systems. In Proceedings of the Royal Society of London, A, 352, 25–40.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Newland, D. E. (1989). Mechanical vibration analysis and computation (pp. 226–257). New York: Academic Press.Google Scholar
  13. 13.
    D’Annibale, F., Ferretti, M., & Luongo, A. (2016). Improving the linear stability of the Beck’s beam by added dashpots. International Journal of Mechanical Sciences, 110, 151–159.CrossRefGoogle Scholar
  14. 14.
    Zamani, V., Kharazmi, E., & Mukherjee, R. (2015). Asymmetric post-flutter oscillations of a cantilever due to a dynamic follower force. Journal of Sound and Vibration, 340, 253–266.CrossRefGoogle Scholar
  15. 15.
    Kirillov, O. N., & Verhulst, F. (2010). Paradoxes of dissipation-induced destabilization or who open Whitney’s umbrella? Zeitschrift für Angewandte Mathematik und Mechanik, 90(6), 462–488.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kirillov, O. N. (2013). Nonconservative stability problems of modern physics. Berlin: De Gruyter.CrossRefGoogle Scholar
  17. 17.
    Bigoni, D., Misseroni, D., Tommasini, M., Kirillov, O. (2018). Detecting singular weak-dissipation limit for flutter onset in reversible systems. Physical Review, E, 97, 023003.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yoshihiko Sugiyama
    • 1
    Email author
  • Mikael A. Langthjem
    • 2
  • Kazuo Katayama
    • 3
  1. 1.Small Spacecraft Systems Research Center, Osaka Prefecture UniversitySakaiJapan
  2. 2.Department of Mechanical Systems EngineeringYamagata UniversityYonezawaJapan
  3. 3.Daicel CorporationTatsunoJapan

Personalised recommendations