A disk of inner radius a and outer radius b is subjected to an angular velocity OJ. The di...

A disk of inner radius a and outer radius b is subjected to an angular velocity OJ. The disk is constrained at r =a, so that the radial displacement u is zero. At r = b, the disk is free of applied forces. Derive formulas for the constants of integration C1 and C2 (see Eqs. 11.47, 11.49, and 11.50), as functions of ω, the material properties ρ, E, and v and the radii a and b. Note that with C1 and C2 , the displacement u and stresses σrr and σθθ are also given as functions of r, etc.

 (11.47)

 (11.49)

 (11.50)