Abstract
The stability behavior of a cantilevered shaft, rotating at a constant speed and subjected to a follower force at the free end, is studied by the finite element method. The equations of motion for such a gyroscopic system are formulated by using deformation shape functions developed from Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformations are included. In order to determine the critical load of the present nonconservative system more quickly and efficiently, a simple and direct method that utilizes the eigenvalue sensitivity with respect to the follower force is introduced. The numerical results show that for the present nonconservative system, the onset of flutter instability occurs when the first and second backward whirl speeds are coincident. And also, due to the effect of the gyroscopic moments, the critical flutter load decreases as the rotational speed increases.