208 Mr Chree, On thin rotating isotropic disks. [May 4, 



Substituting the expressions found for the arbitrary constants in 

 terms of E and 77 in (16), we find for the strains in an annular 

 disk 



S = ^% m {(3 + i){a? + a 2 ) - 2 (1+ v ) r 2 } 



+ g VV-2V)( 1 + V) (P ._ 3/) (29 ) ; 



-^ 2 r^ ( * W) •••- (30) ' 



= g |(1 - *7>(-3 + ^(a 2 + a' 2 ) r - (1 - V 2 ) r 3 + ~ (1 + v)(o + ,)} 



+ ^(l +*,)?• (Z 2 -3* 2 ) (31)- 



From these strains we find for the stresses 

 S = ^ /9 .4- ^ L 2 4- ffl * - •* _ ^1 



M 



(3 + 7/)ja 2 +a' 2 -r 



r 



+ ^^(Z 2 ~-V) (32), 



= -. + ^|(l_^)y + ( 3 + 97 )^i (33). 



For a complete disk we have 



4# 



8 = "V(l_2?) K3 + iy)a ._ 2(1 + iy) > 1 



+ 3^^ (1 "l- ( , 1+??) ^- 8 ^ < 84 >' 



W = -H^K3 + ^^-2(l + ^r^} 



-^ 2 i-~^ 2 -* 2 > ^ 



^ = H(l-^){(3 + ^aV-(H-^)r 3 } 



+ ^|^(l + ^)r(Z 2 -3^) (36), 



p =s !!4 ( 8 + ^)(fl-_0 + ^ily^(« , -80 (37), 



$? = ^ + ^(l-^)r 2 , (38). 



