Stability Behavior of a Shaft-Disk System Subjected to Longitudinal Force

Abstract

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. Nomenclature A = area of cross section of the shaft ai, bi = coefe cients given by Eqs. (21) and (22), respectively Ci, ¯ Ci = integration constants E = Young’ s modulus G = shear modulus hi = coefe cients given by Eq. (26) I = moment of inertia of the shaft cross section ID, IP = diameter and polar mass moments of inertia of the disk ¯D = nondimensional diameter mass moment of inertia of the disk Id, Ip = diameter and polar moments of inertia per unit length of the shaft j = 1 L = length of the shaft L1 = distance between the left end and the intermediate disk