image (5.30)

Inserting (5.25) into (5.30), a second-order differential equation for the determination of τr(r) results. The solution depends on materials properties through ρ, Y, and μ and on the state of rotation through ω. Once the radial stress is determined, the tangential one can be evaluated from (5.25).

As an example, consider a plane disc of radius rmax, with a center hole of radius rmin. In this case, the derivatives of b(r) vanish, and the solution to (5.30) and (5.25) is

τr(r)=(3+μ)ρω2(rmin2+rmax2rmin2rmax2/r2r2)/8τt(r)=(3+μ)ρω2(rmin2+rmax2+rmin2rmax2/r2(1+3μ)r2/(3+μ))/8. (5.31)

(5.31)

The radial stress rises from zero at the inner ...

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