On mode shapes of a stability problem

This paper presents data of mode shapes of some stable and unstable modes of a free-free beam under direction controlled thrusts. These mode shapes are pertinent in understanding this basic problem and hitherto were not available in the literature. It has been found that the node number of the mode shape corresponding to the first divergence mode increases with the magnitude of the thrust. The main feature of the solution method is given. The instability of a free-free beam under a thrust fixed in direction is pointed out.