Radial-displacement solution for a rotating disc with a hyperbolic thickness profile

Abstract

Abstract

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.