The stability behavior of a spinning Timoshenko shaft with an intermediate attached disk subjected to a longitudinal force is analytically studied. The expressions of frequency (whirl speed) equations for hinged-hinged, hinged-clamped, clamped-hinged, and clamped-clamped rotors are given. By using the numerical technique, the critical axial and follower loads are sought. Numerical results reveal that the instability mechanisms are complex. Eight 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 longitudinal loads are almost zero; therefore, such a rotor combination is extremely unstable and should be avoided for design purposes.
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