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)


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

Get Renewable Energy, 5th Edition now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.