Abstract
An elastic cantilevered beam subjected to a follower force, the so-called Beck’s column , is an ideal/classical structural model in the theory of nonconservative stability problems. The stability of columns associated with follower forces is a relatively new topic in the field of structural stability, at least in comparison with the part dealing with conservative forces. This chapter discusses the basic aspects of a column under a follower force, its positive and negative features.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bolotin, V. V. (1963). Nonconservative problems of the theory of elastic stability. New York: Pergamon Press.
Beck, M. (1952). Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes. Zeitschrift für Angewandte Mathematik und Physik, 3, 225–228.
Timoshenko, S. P., & Gere, J. M. (1961). Theory of elastic stability. New York: McGraw-Hill (New York: Dover Publications, Inc., 2009).
Sugiyama, Y., Katayama, T., & Sekiya, T. (1970). Studies on nonconservative problems of instability of columns by difference method. In Proceedings of the 19th Japan National Congress for Applied Mechanics 1969 (pp. 23–31). Tokyo: The University of Tokyo Press.
Sugiyama, Y., Fujiwara, N., & Sekiya, T. (1969). Studies on nonconservative problems of instability of columns by means of analog computer. In Proceedings of the 18th Japan National Congress for Applied Mechanics 1968 (pp. 113–126). Tokyo: The University of Tokyo Press.
Leipholz, H. (1970). Stability theory. New York: Academic Press.
Ziegler, H. (1968). Principles of structural stability. Massachusetts: Blaisdell Publishing Co.
Leipholz, H. (1980). Stability of elastic systems. Alphen aan den Rijn: Sijthoff & Noordhoff.
Langthjem, M. A., & Sugiyama, Y. (2000). Dynamic stability of columns subjected to follower loads: A survey. Journal of Sound and Vibration, 238(5), 809–851.
Elishakoff, I. (2005). Controversy associated with the so-called follower forces. Applied Mechanics Review, 58, 117–142.
Datta, P. K. (2011). Aeroelastic behaviour of aerospace structural elements with follower force: A review. International Journal of Aeronautical and Space Sciences, Korean Society of Aeronautical and Space Sciences, 12(2), 134–148.
Venkateswara Rao, G., & Singh, G. (2001). Revisit to the stability of a uniform cantilever column subjected to Euler and Beck loads—Effect of realistic follower forces. Indian Journal of Engineering and Materials Sciences, 8, 123–128.
Koiter, W. T. (1996). Unrealistic follower forces. Journal of Sound and Vibration, 194(4), 636–638.
Sugiyama, Y., Langthjem, M. A., & Ryu, B.-J. (1999). Realistic follower forces. Journal of Sound and Vibration, 225(4), 779–782.
Sugiyama, Y., Ryu, S.-U., & Langthjem, M. A. (2002). Beck’s column as the ugly duckling. Journal of Sound and Vibration, 254(2), 407–410.
Ziegler, H. (1952). Die Stabilitätskrierien der Elastomechnik. Ingeniur-Archiv, 20, 45–56.
Farrar, D. J. (1956). Structures. The Aeronautical Journal, the Royal Aeronautical Society, 60, 712–720.
Feodosiev, V. I. (1965). On a problem of stability. Prikladnaya Mathematica i Mekhanika, 29, 391–392. (in Russian).
Beal, T. R. (1965). Dynamic stability of a flexible missile under the constant and pulsating thrust. AIAA Journal, 3, 486–494.
Wu, J. J. (1975). On the stability of a beam under axial thrust subjected to directional control. Journal of Sound and Vibration, 42, 45–52.
Wu, J. J. (1976). On missile stability. Journal of Sound and Vibration, 49, 141–147.
Wu, L., Xie, C., & Yang, C. (2012). Aeroelastic stability of a slender missile with constant thrust. Procedia Engineering, 31, 128–135.
Ohshima, T., & Sugiyama, Y. (2003). Dynamic stability of free-free beam subjected to end rocket thrust and carrying a heavy payload at its nose. In Proceedings of 2003 International Conference on Physics and Control (PhysCon 2003) (Vol. 4, pp. 1115–1120). St. Petersburg.
Chae, S. (2004). Effect of follower forces on aeroelastic stability of flexible structures, (Doctoral Thesis). School of Aerospace Engineering, Georgia Institute of Technology, ProQuest Information and Learning Company, Ann Arbor.
Nishiwaki, M. (1993). Generalized theory of brake noise. Proceedings of the Institution of Mechanical Engineers, 207, 195–202.
Mottershead, J. E., & Chan, S. N. (1995). Flutter instability of circular discs with frictional follower loads. Journal of Vibration and Acoustics, 117, 161–163.
Bigoni, D., & Noselli, G. (2011). Experimental evidence of flutter and divergence instabilities induced by dry friction. Journal of the Mechanics and Physics of Solids, 59(10), 2208–2226.
Kurnik, W., Przybylowicz, P. M., & Bogacz, W. (2018). Bigoni and Noseli’s experiment: Is it evidence for flutter in the Ziegler column? Archive of Applied Mechanics, 88, 203–213.
Fazelzadeh, S. A., Karimi-Nobandegani, A., & Mardanpour, P. (2017). Dynamic stability of pretwisted cantilever beams subjected to distributed follower force. AIAA Journal, 55(5), 955–964.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Sugiyama, Y., Langthjem, M.A., Katayama, K. (2019). Columns under a Follower Force. In: Dynamic Stability of Columns under Nonconservative Forces. Solid Mechanics and Its Applications, vol 255. Springer, Cham. https://doi.org/10.1007/978-3-030-00572-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-00572-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00571-9
Online ISBN: 978-3-030-00572-6
eBook Packages: EngineeringEngineering (R0)