The critical speeds of a spinning Timoshenko shaft with an intermediate attached disk subjected to a longitudinal force are analytically solved. The expressions of whirl speed equations for hinged-hinged, hinged-clamped, clamped-hinged, and clamped-clamped rotors are given respectively. The critical speeds of each shaft-disk system are sought from its corresponding whirl speed equation by using simple numerical techniques. The effects of the disk location and the longitudinal force on the critical speeds of the shaft-disk systems are investigated. Numerical results reveal that if the disk locates in the left portion of the shaft, both the primary forward and backward critical speeds for the rotor subjected to a follower force are larger than those subjected to an axial force with the same magnitude. The results are contrary while the disk locates in the right portion of the shaft.

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