Browse > Article
http://dx.doi.org/10.5050/KSNVE.2016.26.6.635

Structural Damping Effects on Stability of a Cantilever Column under Sub-tangentially Follower Force  

Min, Dong-Ju (Sungkyunkwan University)
Park, Jae-gyun (Dankook University)
Kim, Moon-Young (Sungkyunkwan University)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.26, no.6_spc, 2016 , pp. 635-643 More about this Journal
Abstract
A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck's column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.
Keywords
Structural Damping; Follower Force; Stability Map; Flutter; Beck's Column;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Kim, M.-Y., Lee, J.-S. and Attard, M. M., 2013, Stability of Damped Columns on a Winkler Foundation Under Sub-tangential Follower Forces, International Journal of Structural Stability and Dynamics, Vol. 13, No. 2, pp. 1~27.
2 Detinko, F. M., 2003, Lumped Damping and Stability of Beck Column with a Tip Mass, International Journal of Solids and Structures, Vol. 40, No. 17, pp. 4479~4486.   DOI
3 Wolfram, S., 1991, MATHEMATICA, 2nded, Addison-Wesley, Reading, MA.
4 Elishakoff, I., Kaplunov, J. and Nolde, E., 2015, Celebrating the Century of Timoshenko’s Study of Effects of Shear Deformation and Rotary Inertia, Applied Mechanical Reviews, Vol. 67, No. 6, 060802-1–060802-11.   DOI
5 Beck, M., 1952, Die Knicklast des Einseitig Eingespannten, Tangential Gedrückten Stabes, Zeitschrift Für Angewandte Mathematik und Physik, Vol. 3, No. 6, pp. 476~477.   DOI
6 Ziegler, H., 1968, Principles of Structural Stability, Blaisdell Publishing Company, Waltham, Massachussetts.
7 Bolotin, V. V., 1963, Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, NewYork.
8 Rao, B. N. and Rao, G. V., 1990, Stability of a Cantilever Column under a Tip-concentrated Sub-tangential Follower Force with Damping, Journal of Sound and Vibration, Vol. 138, No. 2, pp. 341~344.   DOI
9 Vitaliani, R. V., Gasparini, A. M. and Saetta, A. V., 1997, Finite Element Solution of the Stability Problem for Nonlinear Undamped and Damped System sunder Non-conservative Loading, International Journal of Solids and Structures, Vol. 34, No. 19, pp. 2497~2516.   DOI
10 Sugiyama, Y. and Langthjem, M. A., 2007, Physical Mechanism of the Destabilizing Effect of Damping in Continuous Non-conservative Dissipative Systems, Physical Mechanism of the Destabilizing Effect of Damping in Continuous Non-conservative Dissipative Systems, Vol. 42, No. 1, pp. 132~145.   DOI
11 Kirillov, O. N. and Verhulst, F., 2010, Paradoxes of Dissipation-induced Destabilization or Who Opened Whitney’s Umbrella?, Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 90, No. 6, pp. 462~488.   DOI
12 Leipholz, H. H. E., 1980, Stability of Elastic Systems, SijthotI & Noordhoff, Rijn, The Netherlands.
13 Luongo, A., D’Annibale, F., 2014, On the Destabilizing Effect of Damping on Discrete and Continuous Circulatory Systems, Journal of Sound and Vibration, Vol. 333, No. 24, pp. 6723~6741.   DOI
14 Lee, S. Y., Chen, T. Y. and Wang, W. R., 1980, Non-conservative Instability of a Timoshenko Beam Subjected to a Partially Tangential Follower Force, Journal of Sound and Vibration, Vol. 188, No. 1, pp. 25~38.   DOI
15 Sundararamaiah, V. and Venkateswara Rao, G., 1983, Stability of Short Beck and Leipholz Column on Elastic Foundation, AIAA Journal, Vol. 21, No. 7, pp. 1053~1054.   DOI
16 Chen, L.-W. and Ku, D.-M., 1991, Stability Analysis of a Timoshenko Beam Subjected to Distributed Follower Forces Using Finite Elements, Computers and Structures, Vol. 41, No. 4, pp. 813~819.   DOI
17 Ryu, B. J., Katayama, K. and Sugiyama, Y., 1998, Dynamic Stability of Timoshenko Columns Subjected to Sub-tangential Forces, Computers and Structures, Vol. 68, No. 5, pp. 499~512.   DOI
18 Attard, M. M., Lee, J.-S. and Kim, M.-Y., 2008, Dynamic Stability of Shear-flexible Beck’s Columns based on Engesser’s and Haringx’s Buckling Theories, Computers and Structures, Vol. 86, No. 21-22, pp. 2042~2055.   DOI
19 Langthjem, M. A. and Sugiyama, Y., 2000, Dynamic Stability of Columns Subjected to Follower Loads: a Survey, Journal of Sound and Vibration, Vol. 238, No. 5, pp. 809~851.   DOI
20 Elishakoff, I., 2005, Controversy Associated with the So-called Follower Forces: Critical Overview, Appl. Mech. Reviews, Vol. 58, No. 2, pp. 117~142.   DOI
21 Lee, J.-S., Kim, N.-I. and Kim, M.-Y., 2007, Sub-tangentially Loaded and Damped Beck’s Columns on Two-parameter Elastic Foundation, Journal of Sound and Vibration, Vol. 306, No. 3-5, pp. 766~789.   DOI
22 Lee, B. K., Li, G., Oh, S. J. and Kim, G. S., 2005, Stability Analysis of Beck’s Column with a Tip Mass Restrained by a Spring, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 15, No. 11, pp. 1287~1294.   DOI
23 Andersen, S. B. and Thomsen, J. J., 2002, Post-critical Behavior of Beck's Column with a Tip Mass, International Journal of Nonlinear Mechanics, Vol. 37, No. 1, pp. 135~151.   DOI