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An analytical investigation was made on the effect of axial torque on the critical speeds of a continuous rotor whose motion was described by a set of partial differential equations including the effects of transverse shear, rotatory inertia, and gyroscopic moments. The equations of motion and associated boundary conditions for long and short bearings were cast in nondimensional form to facilitate the study of the influence of the aforementioned effects on a torque-transmitting rotor’s critical speeds. The results of this study were compared to classical results of Bernoulli-Enter and Timoshenko to determine the relative importance of the rotor’s “secondary phenomena” in a critical speed calculation.

The effect of gyroscopic moments on the critical speeds of a shaft-disk system mounted in short end bearings is investigated. Representation of the shaft as having continuously distributed mass and elasticity allows accurate determination of higher critical speeds. Frequency equations are obtained for the critical speeds associated with both backward and forward whirling modes. The first four critical speeds (backward and forward whirling modes) are given for a range of shaft and disk sizes and for various disk locations on the shaft. Experimental verification is given for the first and second critical speeds.

An explicit series solution is presented for the stress and displacement fields in an elastic body of infinite extent containing two equidiameter spherical cavities. At large distances from the cavities the displacement field coincides with that which arises from pure torsion about the axis of symmetry. Numerical results are presented in graphs which demonstrate the interference of the two sources of stress concentration.