Stability of nonconservative systems using eigenvalue sensitivity

The finite-element method and the technique of eigenvalue sensitivity are both applied to the stability analysis of a cantilever column subjected to a follower force at the free end. In the finite-element formulation, the shape functions that contain a shear deformation parameter are developed from Timoshenko beam theory, and the effects of transverse shear deformation and rotary inertia are also included. The advantage of such a formulation is that if suitable values of parameters are given, then a specific beam model is simulated without too much additional work to modify the original formulation. In order to determine the critical load of such a nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. Numerical results show that the critical load calculated by this method not only has an excellent agreement compared with the previously published work, but also the rate of convergence is quite fast.