2 2 parr t B pw2r2
The only difference to the previous treatment is the conditions which are required to evaluate the constants A and B since, in this case, B is not zero.
The above equations are similar in form to the Lamé equations for pressurised thick rings or cylinders with modifying terms added. Indeed, should the condition arise in service where a rotating ring or cylinder is also pressurised, then the pressure and rotation boundary conditions may be substituted simultaneously to determine appropriate values of the constants A and B.
However, returning to the rotation only case, the required boundary conditions are zero radial stress at both the inside and outside radius, i.e. at r = R<
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