Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Dynamic Stability of a Cantilevered Timoshenko Beam on Partial Elastic Foundations Subjected to a Follower Force

  • Ryu, Bong-Jo (Department of Mechanical Design Engineering, Hanbat National University) ;
  • Shin, Kwang-Bok (Department of Mechanical Design Engineering, Hanbat National University) ;
  • Yim, Kyung-Bin (Department of Mechanical Engineering, Dongyang Technical College) ;
  • Yoon, Young-Sik (Department of Mechanical Engineering, Konyang University)
  • Published : 2006.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents the dynamic stability of a cantilevered Timoshenko beam with a concentrated mass, partially attached to elastic foundations, and subjected to a follower force. Governing equations are derived from the extended Hamilton's principle, and FEM is applied to solve the discretized equation. The influence of some parameters such as the elastic foundation parameter, the positions of partial elastic foundations, shear deformations, the rotary inertia of the beam, and the mass and the rotary inertia of the concentrated mass on the critical flutter load is investigated. Finally, the optimal attachment ratio of partial elastic foundation that maximizes the critical flutter load is presented.

Keywords

References

  1. Anderson, G. L., 1975, 'The Influence of Rotary Inertia, Tip Mass, and Damping on the Stability of a Cantilever Beam on an Elastic Foundation,' Journal of Sound and Vibration, 43, pp. 543-552 https://doi.org/10.1016/0022-460X(75)90006-1
  2. Chen, L. W. and Ku, D. M., 1992, 'Stability of Elastic Systems Under Follower Forces,' AIAA Journal, 30, pp.767-771 https://doi.org/10.2514/3.10983
  3. Elishakoff, I. and Wang, X., 1987, 'Generalization of Smith-Herrmann Problem with the aid of Computerized Symbolic Algebra,' Journal of Sound and Vibration, 117, pp. 537-542 https://doi.org/10.1016/S0022-460X(87)80072-X
  4. Hauger, W. and Vetter, K., 1976, 'Influence of an Elastic Foundation on the Stability of a Tangentially Loaded Column,' Journal of Sound and Vibration, 47, pp. 296-299 https://doi.org/10.1016/0022-460X(76)90726-4
  5. Jacoby, A. and Elishakoff, I., 1986, 'Discrete-Continuous Elastic Foundation may Leave the Flutter Load of the Pfluger Column Unaffected,' Journal of Sound and Vibration, 108, pp. 523-525 https://doi.org/10.1016/0022-460X(76)90726-4
  6. Langthjem, M. A. and Sugiyama, Y., 2000, 'Dynamic Stability of Columns Subjected to Follower Loads: a Survey,' Journal of Sound and Vibration, 238, pp. 809-851 https://doi.org/10.1006/jsvi.2000.3137
  7. Maurizi, M. J. and Bambill, E. A., 2002, 'An Additional Note on Dynamic Stability of Columns Subjected to Follower Loads: a Survey,' Journal of Sound and Vibration, 251, pp. 181-183 https://doi.org/10.1006/jsvi.2001.3785
  8. Smith, T. E. and Herrmann, G., 1972, 'Stability of a Beam on an Elastic Foundation Subjected to a Follower Force,' Journal of Applied Mechanics, 39, pp. 628-629 https://doi.org/10.1115/1.3422743
  9. Sundararajan, C., 1974, Stability of Columns on Elastic Foundations Subjected to Conservative and Non-conservative Forces,' Journal of Sound and Vibration, 37, pp. 79-85 https://doi.org/10.1016/S0022-460X(74)80059-3
  10. Sundararajan, C., 1976, 'Influence of an Elastic end Support on the Vibration and Stability of Beck's Column,' International Journal of Mechanical Science, 18, pp. 239-241 https://doi.org/10.1016/0020-7403(76)90005-9