Stability analyses of a Timoshenko shaft with dissimilar lateral moments of inertia

The stability of a rotating shaft with dissimilar stiffnesses is studied and the influences of the stiffness ratio and axial compressive loads are discussed. A finite element model of a Timoshenko beam is adopted to approximate the shaft, and the effects of rotatory inertia, shear deformations, gyroscopic moments and torsional rigidities are taken into account. In studying the whirl properties of such shafts, it is convenient to use rotating co-ordinates to formulate the equations of motion. The results show that with the existence of the dissimilar stiffnesses, unstable zones will occur. The critical speeds will decrease and the instability regions will enlarge if the stiffness ratio is increased. The increase of the stiffness ratio consequently makes the rotating shaft more unstable. When the axial compressive loads increase, the critical speeds decrease and the zones of instability enlarge.