Critical Loads of Tapered Beck's Columns with Clamped and Spring Supports

일단고정 타단스프링으로 지지된 변단면 Beck 기둥의 임계하중

  • 김석기 (단국대학교 토목환경공학과) ;
  • 박광규 (대전대학교 토목공학과) ;
  • 이병구 (원광대학교 토목환경공학과)
  • Published : 2006.03.01

Abstract

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

References

  1. 이병구, 진태기, 이태은 (2002) 크로소이드 완화곡선을 갖는 수평 곡선보의 자유진동, 한국전산구조공학회논문집, 15(1), pp.189-195
  2. Beck, M.(1952) Die Knicklast Des einseitig eingespannten, tangential gedruckten Stabes, Zeitschrift fur Angewandte Mathematik und Physik. 3. pp.225-228 https://doi.org/10.1007/BF02008828
  3. Bokaian, A.(1988) Natural frequencies of beams under compressive axial loads. Journal of Sound and Vibration, 126. pp.49-65 https://doi.org/10.1016/0022-460X(88)90397-5
  4. Chen, L.W. Ku, D.M.(1992) Eigenvalue sensitivity in the stability analysis of Beck's column with a concentrated mass at the free end. Journal of Sound and Vibration, 153, pp.403-411 https://doi.org/10.1016/0022-460X(92)90373-6
  5. Koiter, W.T.(1996) Unrealistic follower forces, Journal of Sound and Vibration, 194, pp.636-638 https://doi.org/10.1006/jsvi.1996.0383
  6. Kounadis, A. Katsikadelis, J.T. (1976) Shear and rotatory inertia effect on Beck's column. Journal of Sound and Vibration, 49, pp.171-178 https://doi.org/10.1016/0022-460X(76)90494-6
  7. Kuo, S.R. Yang, Y.B.(1994) Critical load analysis of undamped non-conservative systems using bieigenvalue curves. AIAA Journal, 32, pp.2462-2468 https://doi.org/10.2514/3.12314
  8. Kupta, A.K. (1985) Vibrations of tapered beams. Journal of Structural Engineering, ASCE, 113, pp. 1244-1247
  9. Langthiem, A., Sugiyama, Y.(1999) Optimum shape design against flutter of a cantilevered column with an end-mass of finite size subjected to a non-conservative load. Journal of Sound and Vibration, 226, pp.1-23 https://doi.org/10.1006/jsvi.1999.2211
  10. Lee, B.K., Oh, S.J.(2000) Elastica and buckling load of simple tapered columns with constant volume. International Journal of Solids and Structures, 37, pp.2507-2518 https://doi.org/10.1016/S0020-7683(99)00007-4
  11. Pedersen, P.(1977) Influence of boundary conditions on the stability of a column under non-conservative load. International Journal of Solids and Structures. 13. pp.445-455 https://doi.org/10.1016/0020-7683(77)90039-7
  12. Ryu, B.J., Sugiyama, Y., Lee, G.S.(1997) The influence of an intermediate support on the dynamic stability of cantilevered Timoshenko beams subjected to subtangential forces. Proceedings of Asia-Pacific Vibration Conference '97, Kyongju, Korea, pp.163-168
  13. Sankaran, G.V., Rao, G.V. (1976) Stability of tapered cantilever columns subjected to follower forces. Computers and Structures, 6, pp.217-220 https://doi.org/10.1016/0045-7949(76)90033-X
  14. Sato, K.(1996) Instability of a clamped-elastically restrained Timoshenko column carrying a tip load, subjected to a follower force, Journal of Sound and Vibration, 194, pp.623-630 https://doi.org/10.1006/jsvi.1996.0381
  15. Sugiyama, Y., Langthjem, M.A., Ryu, B.J. (1999) Realistic follower forces, Journal of Sound and Vibration, 225, pp.779-782 https://doi.org/10.1006/jsvi.1998.2290