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Beam stability on an elastic foundation subjected to distributed follower force

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Abstract

Problems related to the stability and behavior of a cantilevered beam with a tip mass on an elastic foundation and subjected to a distributed follower force are addressed. The stability of a beam partially attached to an elastic foundation is also considered. The dynamic stability of a beam subjected to a distributed follower force is formulated by using finite element method to get a general eigenvalue problem. The influence of the modulus on the elastic foundation and the ratio of the cantilevered beam’s mass to the tip mass on the critical flutter are investigated. Finally, the stability of the cantilevered beam is found to depend on both the modulus of the elastic foundation and the ratio of the cantilevered beam’s mass to the tip mass.

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Reference

  1. M. Beck, Die Knicklast des Einseitig Eingespannten, Tangential Gedrückten Stabes, ZAMP 3(3) (1952) 225–228.

    Article  MATH  Google Scholar 

  2. A. Pflüger, Zur Stabilität des Tangential gedrückten Stabes, ZAMM 35(5) (1955) 191.

    Article  MATH  Google Scholar 

  3. H. Leipholz, Die Knicklast des einseitig eingespannten Stabes mit gleichmässig verteilter, tangentialer Längsbelastung, ZAMP 13 (1962) 581–589.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. A. Langthjem and Y. Sugiyama, Dynamic Stability of Columns Subjected to Follower Loads: A Survey, Journal of Sound and Vibration 238 (2000) 809–851.

    Article  Google Scholar 

  5. T. E. Smith and G. Herrmann, Stability of a Beam on an Elastic Foundation Subjected to Follower Forces, Journal of Applied Mechanics 39 (1972) 628–629.

    Article  Google Scholar 

  6. G. L. Anderson, The Influence of Rotatory Inertia, Tip Mass, and Damping on the Stability of a Cantilever Beam on an Elastic Foundation, Journal of Sound and Vibration 43(3) (1975) 543–552.

    Article  MATH  Google Scholar 

  7. H. I. Yoon and K. S. Kim, The Influence of Inertial Moment of Tip Mass on the Stability of Beck’s Column, Transactions of the Korea Society of Mechanical Engineers 8(2) (1984) 119–126.

    Google Scholar 

  8. S. Y. Lee and Y. H. Kuo and F. Y. Lin,, Stability of a Timosenko Beam Resting on a Winkler Elastic Foundation, Journal of Sound and Vibration 153(2) (1992) 193–202.

    Article  MATH  Google Scholar 

  9. M. J. Maurizi, and E. A. Bambill, An Additional Note on “Dynamic Stability of Columns Subjected to Follower Loads: A Survey” (M. A. Langthjem and Y. Sugiyama, Journal of Sound and Vibration 238 (2000) 809–851), Journal of Sound and Vibration 251(1) (2002) 181–183.

    Article  Google Scholar 

  10. J. H. Sällström, Fluid-Conveying Beams in Transverse Vibration, Doctoral Dissertation, Division of Solid Mechanics, Chalmers University of Technology (1992).

  11. Y. Sugiyama and H. Kawagoe, Vibration and stability of elastic columns under the combined action of uniformly distributed vertical and tangential forces, Journal of Sound and Vibration 38 (1975) 314–355.

    Article  MATH  Google Scholar 

  12. Y. Sugiyama and K. A. Mladenov, Vibration and stability of elastic columns subjected to triangularly distributed subtangential forces, Journal of Sound and Vibration 88 (1983) 447–457.

    Article  Google Scholar 

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Authors and Affiliations

  1. Division of Architectural Engineering Hanbat National University, San 16-1, Dukmyung, Yuseong-gu, Daejeon, 305-719, Korea

    Jae-On Kim

  2. Mechanical Engineering at Chungnam National University, 220, Gungdong, Yuseong-gu, Daejeon, 305-764, Korea

    Kee-Seok Lee & Jin-Woo Lee

Authors
  1. Jae-On Kim
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  2. Kee-Seok Lee
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  3. Jin-Woo Lee
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Corresponding author

Correspondence to Kee-Seok Lee.

Additional information

This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo

Dr. Jae-On Kim is now adjunct professor of Hanbat National University and president of Shinwall architectural & const. Co. Ltd. He has an excellent background in the architecural structure design and analysis.

Dr. Kee-Seok Lee was educated at the Chungnam National University in Korea Ph.D. degree in mechanical engineering. For 10 years, he has a researcher in the field of mechanical design and control. Especially, he has an excellent background in the vibration control. At university, he has designend and established the control method for measuring Cam Profile without contact and air-bearing control method under disturbances. He is an author of 10 papers.

Dr. Jin-Woo Lee was educated at the Kyushu institute of Technology in JapanPh.D. degree in of life-science and system engineering(Dec., 2006). He is a senior researcher at the steel solution research group of POSCO.

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Kim, JO., Lee, KS. & Lee, JW. Beam stability on an elastic foundation subjected to distributed follower force. J Mech Sci Technol 22, 2386–2392 (2008). https://doi.org/10.1007/s12206-008-0823-9

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  • DOI: https://doi.org/10.1007/s12206-008-0823-9

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