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

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.