Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
권호 표지

Influence of Partial Elastic Foundations on Dynamic Stability of a Cantilevered Timoshenko Beam with a Tip Mass under a follower force

끝단 질량을 갖고 종동력을 받는 외팔 Timoshenko 보의 동적안정성에 미치는 부분 탄성기초의 영향

  • Published : 2005.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam with a tip concentrated mass is assumed to be a Timoshenko beam taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and finite element method is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, rotary inertia of the beam and magnitude and rotary inertia of the tip mass is fully investigated.

Keywords

References

  1. Smith, T. E. and Herrmann, G., 'Stability of a Beam on an Elastic Foundation Subjected to a Follower Force,' Journal of Applied Mechanics, Vol. 39, pp. 628-629, 1972 https://doi.org/10.1115/1.3422743
  2. Sundarajan, C., 'Stability of Columns on Elastic Foundations Subjected to Conservative and Non-conservative Forces,' Journal of Sound and Vibration, Vol. 37, pp. 79-85, 1974 https://doi.org/10.1016/S0022-460X(74)80059-3
  3. Anderson, G. L., '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, Vol. 43, pp. 543-552, 1975 https://doi.org/10.1016/0022-460X(75)90006-1
  4. Hauger, W. and Vetter, K., 'Influence of an Elastic Foundation on the Stability of a Tangentially Loaded Column,' Journal of Sound and Vibration, Vol. 47, pp. 296-299, 1976 https://doi.org/10.1016/0022-460X(76)90726-4
  5. Sundararajan, C., 'Influence of an Elastic End Support on the Vibration and Stability of Beck's Column,' International Journal of Mechanical Science, Vol. 18, pp. 239-241, 1976 https://doi.org/10.1016/0020-7403(76)90005-9
  6. Jacoby, A. and Elishakoff, I., 'Discrete-continuous Elastic Foundation may leave the Flutter Load of the Pfluger Column Unaffected,' Journal of Sound and Vibration, Vol. 108, pp. 523-525, 1986 https://doi.org/10.1016/S0022-460X(86)80045-1
  7. Elishakoff, I. and Wang, X., 'Ge neralization of Smith-Herrmann Problem with the Aid of Computerized Symbolic Algebra,' Journal of Sound and Vibration, Vol. 117, pp. 537-542, 1987 https://doi.org/10.1016/S0022-460X(87)80072-X
  8. Chen, L. W. and Ku, D. M., 'Stability of Elastic Systems under Follower Forces,' AIAA Journal, Vol. 30, pp. 767-771, 1992 https://doi.org/10.2514/3.10983
  9. Lee, S. Y., Kuo, Y. H. and Lin, F. Y., 'Stability of a Timoshenko Beam Resting on a Winkler Elastic Foundation,' Journal of Sound and Vibration, Vol. 153, pp. 193-202, 1992 https://doi.org/10.1016/S0022-460X(05)80001-X
  10. Budkowska, B. B. and Szymczak, C., 'Initial Post-buckling Behavior of Piples Partially Embedded in Soil,' Computers & Structures, Vol. 62, pp. 831-835, 1997 https://doi.org/10.1016/S0045-7949(96)00302-1
  11. Maurizi, M. J. and Bambill, E. A., 'An Additional Note on 'Dynamic Stability of Columns Subjected to Follower Loads : A Survey,' Journal of Sound and Vibration, Vol. 251, pp. 181-183, 2002 https://doi.org/10.1006/jsvi.2001.3785
  12. Langthjem, M. A. and Sugiyama, Y., 'Dynamic Stability of Columns Subjected to Follower Loads : A Survey,' Journal of Sound and Vibration, Vol. 238, pp. 809-851, 2000 https://doi.org/10.1006/jsvi.2000.3137