Skip to main content
SpringerLink
Log in

Dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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.

    Article  MATH  Google Scholar 

  • Chen, L. W. and Ku, D. M., 1992, “Stability of Elastic Systems Under Follower Forces,”AIAA Journal, 30, pp. 767–771.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Design Engineering, Hanbat National University, San 16-1, Duckmyoung-dong, Yuseong-gu, 305-764, Daejeon, Korea

    Bong-Jo Ryu & Kwang-Bok Shin

  2. Department of Mechanical Engineering, Dongyang Technical College, 62-160, Gocheok-dong, Gurogu, 152-714, Seoul, Korea

    Kyung-Bin Yim

  3. Department of Mechanical Engineering, Konyang University, 26, Nae-dong, Nonsan, 320-711, Chungnam, Korea

    Young-Sik Yoon

Authors
  1. Bong-Jo Ryu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kwang-Bok Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyung-Bin Yim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Young-Sik Yoon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bong-Jo Ryu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ryu, BJ., Shin, KB., Yim, KB. et al. Dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. J Mech Sci Technol 20, 1355–1360 (2006). https://doi.org/10.1007/BF02915958

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02915958

Key Words

Search

Navigation