Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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Effects of Slenderness Ratio on Dynamic Behavior of Cracked Beams Subjected to Subtangential Follower Force

경사종동력과 크랙을 가진 보의 진동특성에 미치는 세장비의 영향

  • Son, In-Soo (Department of mechanical Engineering, Dong-eui Univ.) ;
  • Yoon, Han-Ik (Department of mechanical Engineering, Dong-eui Univ.)
  • Published : 2009.09.01
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Abstract

In this paper the purpose is to investigate the stability and variation of natural frequency of a cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the stability of a cantilever beam as the crack effect and slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. By using the results of this paper, we can obtain the judgment base that the choice of beam models for the effect of slenderness ratio and crack.

Keywords

References

  1. Harris, C. M., 'Shock and Vibration Handbook(4thEdition),' McGraw-Hill,Chapter 7, 1961
  2. Igor, A. K. and Olga, I. L., 'Formulas for StructuralDynamics,' McGraw-Hill, Chapter 11, 2001
  3. Kounadis, A. and Katsikadelis, J. T., 'Shear andRotatory Inertia Effect on Beck's Column,' Journal ofSound and Vibration, Vol. 49, No. 2, pp. 171-178, 1976 https://doi.org/10.1016/0022-460X(76)90494-6
  4. Saito, H. and Otomi, K., 'Vibration and Stability ofElastically Supported Beams Carrying an AttachedMass Under Axial and Tangential Loads,' Journal of Sound and Vibration, Vol. 62, No. 2, pp. 257-266, 1979 https://doi.org/10.1016/0022-460X(79)90025-7
  5. Chen, L. W. and Ku, D. M., 'Eigenvalue Sensitivityin the Stability Analysis of Beck's Column with aConcentrated Mass at the Free End,' Journal ofSound and Vibration, Vol. 153, No. 3, pp. 403-411,1992 https://doi.org/10.1016/0022-460X(92)90373-6
  6. Lee, S. Y., Chen, T. Y. and Wang, W. R., 'NonconservativeInstability of a Timoshenko BeamSubjected to a Partially Tangential Follower Force,' Journal of Sound and Vibration, Vol. 188, No. 1, pp.25-38, 1995 https://doi.org/10.1006/jsvi.1995.0576
  7. Sato, K., 'Instability of a Clamped -elasticallyRestrained Timoshenko Columns Carrying a TipLoad, Subjected to a Follower Force,' Journal of Sound and Vibration, Vol. 194, No. 4, pp. 623-630, 1996 https://doi.org/10.1006/jsvi.1996.0381
  8. Lee, B. K., Li, G., Oh, S. J. and Kim, G. S., 'StabilityAnalysis of Beck's Column with a Tip MassRestrained by a Spring,' Transactions of KSNVE, Vol. 15, No. 11, pp. 1287-1294, 2005 https://doi.org/10.5050/KSNVN.2005.15.11.1287
  9. Langthjem, M. A. and Sugiyama, Y., 'OptimumDesign of Cantilevered Columns under the CombinedAction of Conservative and Nonconservative Loads Part I: The Undamped Case,' Computers andStructures, Vol. 74, No. 4, pp. 385-398, 2000 https://doi.org/10.1016/S0045-7949(99)00050-4
  10. Son, I. S., Yoon, H. I. and Ahn, T. S., 'StabilityAnalysis of Cracked Cantilever Beam with Tip Mass and Follower Force,' Transactions of KSNVE, Vol. 17, No. 7, pp. 605-610, 2007 https://doi.org/10.5050/KSNVN.2007.17.7.605
  11. Meirovitch, L.,'Analytical Methods in Vibration,' The Macmillan Company, Chapter 5,1967