An analysis is presented of the stresses and deflections in a circular disk of uniform thickness with various boundary conditions subjected to gyroscopic forces. The derivation of boundary condition equations for three types of disk support are given. These are: a disk fixed or rigidly clamped at its outer periphery, a disk simply supported at its outer periphery and a disk elastically supported at its outer periphery. The effect of the normal component of the centrifugal stresses in the plane of the disk when the disk undergoes bending out of this plane is neglected since this effect always results in a reduction of the stresses and deflections. The results are thus not exact but of value to the design engineer in that they are limiting or maximum values. The results are exact, however, for the case of a disk or plate loaded by a linearly varying symmetrical pressure which duplicates the gyroscopic force distribution. Curves are presented for dimensionless deflection and for radial and tangential bending stress for solid disks and those with central holes up to one half the outer diameter of the disk for the case of simple support and fixed support at the outer periphery. The magnitude of both stresses and deflections is found to be much less than that found by other investigators for the case of a disk rigidly clamped to a shaft. Good agreement was obtained with the results of a recent paper for the solid disk (without central hole). A sample problem is presented to illustrate the general usefulness of the curves for both a gyroscopic loading condition and a corresponding linearly varying symmetrical pressure distribution.
