Constant Thickness Rotating Disk

Abstract

For the constant thickness disk (h = cost; dh/dr = 0), the solving differential equation (1.28) is specialized in the following form:

$$ \frac{{{{d}^2}u}}{{d{{r}^2}}} + \frac{1}{r} \cdot \frac{{du}}{{dr}} - \frac{u}{{{{r}^2}}} - \left( {1 + \nu } \right) \cdot \alpha \cdot \frac{{d{\rm T} }}{{dr}} + \left( {1 - {{\nu }^2}} \right) \cdot \frac{{\gamma \cdot {{\omega }^2} \cdot r}}{E} = 0. $$