Browse > Article

Critical Loads of Tapered Cantilever Columns with a Tip Mass  

Jeong, Jin Seob (원광대학교 토목환경공학과)
Lee, Byoung Koo (원광대학교 토목환경공학과)
Kim, Gwon Sik (원광대학교 대학원)
Kim, Jong Ung (원광대학교 대학원)
Publication Information
Journal of Korean Society of Steel Construction / v.17, no.6, 2005 , pp. 699-705 More about this Journal
Abstract
This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.
Keywords
Beck's column; divergence critical load; flutter critical load; subtangential follower force; tangential follower force;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Stability of tapered cantilever columns subjected to follower forces /
[ Sankaran, G.Y.;Rao, G.V. ] / Computers and Structures
2 Instability of a clamped-elastically restrained Timoshenko column carrying a tip load, subjected to a follower force /
[ Sato, K. ] / Journal of Sound and Vibration
3 Bokaian, A. (1988) Natural frequencies of beams under compressive axial loads, Journal of Sound and Vibration, Vol. 126, pp. 49-65   DOI   ScienceOn
4 Lee, H.P. (1996) Dynamic stability of a tapered cantilever beam on an elastic foundation subjected to a follower force, International Journal of Solids and Structures, Vol. 33, pp. 1409-1424   ScienceOn
5 Pedersen, P. (1977) Influence of boundary conditions on the stability of a column under non-conservative load, International Journal of Solids and Structures, Vol. 13, pp. 445-455   ScienceOn
6 Langthjem, A. and 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, Vol. 226, pp. 1-23   ScienceOn
7 Sankaran, G.Y. and Rao, G.V. (1976) Stability of tapered cantilever columns subjected to follower forces, Computers and Structures, Vol. 6, pp. 217-220   ScienceOn
8 Beck., M (1952) Die Knicklast des einseitig eingespannten, tangential gedruckten Stabes, Zeitschrift für Angewandte Mathematik und Physik, Vol. 3, pp. 225-228
9 Lee, B.K. and Oh, S.J. (2000) Elastica and buckling load of simple tapered columns with constant volume, International Journal of Solids and Structures, Vol. 37, pp. 2507-2518   ScienceOn
10 Chen, L.W. and 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, Vol. 153, pp. 403-411   DOI   ScienceOn
11 Kupta, A.K. (1985) Vibrations of tapered beams, Journal of Structural Engineering, ASCE, Vol. 113, pp. 1244-1247
12 Lee, S.Y. and Yang, C.C. (1993) Non-conservative instability of a Timoshenko beam resting on Winkler elastic founda- tion, Journal of Sound and Vibration, Vol. 162, pp. 177-184   ScienceOn
13 Leipholz, H. (1987) Stability theory, 2nd Edition, John Wiley and Sons
14 류봉조, 임경빈, 이종원, 한재섭 (1999) 2층 탄성기초 위에 놓 인 불균일 테이퍼진 보의 진동과 안정성, 한국소음진동공 학회 논문집, 한국소음진동공학회, 제9권, pp. 828-834
15 이병구, 이태은, 안대순, 김무영 (2001) 두 변수 탄성지반으로 지지된 불연속 변단면 수평 곡선부재의 자유진동, 한국강 구조학회 논문집, 한국강구조학회, 제 13권, 제 6호, pp. 651-659
16 De Rosa, M.A. and Franciosi, C. (1990) The influence of an intermediate support on the stability behaviour of cantilever beams subjected to follower forces, Journal of Sound and Vibration, Vol. 137, pp. 107-115   DOI   ScienceOn
17 Bolotin, V.V. (1964) The dynamic stability of elastic system, Hoden-Day, Inc
18 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, Vol. 194, pp. 623-630