The stability behavior of a non-conservative spinning Timoshenko shaft with an overhung disk

The stability behavior of a spinning Timoshenko shaft with an overhung disk subjected to a follower force is analytically studied. The succinct expression of frequency (whirl speed) equations for hinged-hinged-free and clamped-hinged-free rotors are given. By using the numerical technique, the critical follower loads are sought. Numerical results reveal that the instability mechanisms are complex due to the presence of the spin speed, the overhung disk and the location of the intermediate support. Fifteen different types of instability mechanisms are presented. The critical load jump is possible when the instability mechanism changes from one to another. Furthermore, in some special cases, the critical follower loads are almost zero; therefore, such a rotor combination is extremely unstable and should be avoided for design purposes.