On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 4, 1113 Sofia, Bulgaria
Journal of Sound and Vibration (Impact Factor: 1.81). 04/2008; 311(3):1431-1437. DOI: 10.1016/j.jsv.2007.10.005


The dynamic stability of a cantilevered Timoshenko beam lying on an elastic foundation of Winkler type and subjected to a tangential follower force is studied. Two models describing this phenomenon are examined and their predictions are compared in several special cases. For the values of the beam parameters considered here, the critical compressive forces obtained using these models differ substantially only for short beams as has already been established in other cases. Both models are found to predict dynamic instability of cantilevers under tension unlike the Bernoulli–Euler beam theory. For a beam of intermediate slenderness the Winkler foundation is found to reduce the critical tensile force.

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    • "The changes in the dynamic characteristics, due to the presence of a crack on an axially loaded uniform Timoshenko beam, are investigated by Viola et al. [7]. The dynamic stability of a cantilever Timoshenko beam on an elastic foundation of Winkler type and subjected to a follower force is studied by Djondjorov and Vassilev [8]. The Winkler foundation is found to reduce the critical tensile force for a beam of intermediate slenderness. "
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