Stability analysis of a timoshenko beam subjected to distributed follower forces using finite elements

The stability behavior of a Timoshenko beam subjected to a uniformly distributed follower force is studied by the finite element method. In order to more quickly and efficiently obtain the critical load for such a system, a technique which utilizes the eigenvalue sensitivity with respect to the nonconservative force is introduced instead of the conventional trial-and-error technique. The highly accurate results and rapid rate of convergence through the combination of the present finite element model and the solution algorithm are demonstrated with the numerical examples given.