648 Prof. H. H. Jeffcott on the Whirling Speeds of a 



If we had worked through the constants separately for 

 each load, we should have obtained the results got from the 

 above by putting in turn X/ = and X = 0. 



EI 



Put Xi=?»eo 2 «, X/=m&> 2 v, d> = 188416 — «— «? • 



Thus <f)u = a^u 4- « 2 r, 



Note tbat a 2 =b 1 . 



Eliminating u and v, we find \ 



<£ 2 — (aj + b. 2 )cj) + aj>2 — dj)\ = 0. 



</> 2 -6681<£ + 5269760 = 0. 



6 = 913-7 or 5767-2. 



EI 



a) 2 = (32-7 or 206) x - ? . 



w = (5-72 or 14-36) X \/- 



™/ 3 



The two whirling speeds are respectively of the types 



Fur. 2. 



illustrated in figs. 2 and 3. 



Fkr. 3. 



§ 11. When the number of section changes and loads is 

 large, the constants may conveniently be worked out in 



tabular form, and the values of C l5 Y, Y', -j^-u, -j^~v, be 



also shown in the Table. It will be noted from the general 

 formulae of § 9 that the coefficients of C 1? Y, Y', in the values 

 of the constants corresponding to the several section change 

 points are the same for all the individual loads. Thus only 

 the coefficients of the terms in X or X' and M or M' vary 

 from load to load. As an example the case worked out in 

 § 10 may be arranged in tabular form as follows : 



