The general solution for radial displacement, and thereby radial and circumferential stresses, in a rotating disc having a thickness governed by the law t = Ar−n (which has become generally known as the disc with a hyperbolic profile) covers all cases but one. It is shown in this note that there is a unique thickness profile, produced when n=8/3+v, at which the displacements and stresses become indeterminate. The special solution required for this case is developed below.
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References
1.
StodolaA.Steam and gas turbines (translated by Loewenstein, A.) 1927, 1, 386–388.
