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Mathematical Problems in Engineering
Volume 2016, Article ID 3568970, 15 pages
Research Article

Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

1School of Civil and Architectural Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si 16419, Republic of Korea
2Department of Civil & Environmental Engineering, Dankook University, 126 Jukjeon-dong, Suji-gu, Yongin-si 448-701, Republic of Korea
3Department of Civil Engineering, Semyung University, 579 Sinwoul-dong, Jecheon-si, Chungbuk 390-711, Republic of Korea

Received 14 April 2016; Revised 10 June 2016; Accepted 12 June 2016

Academic Editor: Anders Eriksson

Copyright © 2016 Dong-Ju Min et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A frequency equation of externally and internally damped and shear-flexible cantilever columns subjected to a subtangentially follower force is analytically derived in a dimensionless form with relation to the linear instability theory of Beck’s columns. Some parametric studies are then performed with variation of two damping coefficients under the assumption of Rayleigh damping. Based on the analysis results, it is demonstrated that three damping cases in association with flutter loads of Beck’s columns can be selected including one case representative of structural damping. Finally, stability maps of shear-flexible and damped Beck’s columns are constructed for the three damping cases and discussed in the practical range of damping coefficients and shear parameters. In addition, flutter loads and time history analysis results are presented using dimensionless FE analysis and compared with exact solutions.