438 hersey: alterations of elastic systems 



Subscripts 1 and 2 refer to the members of a coupled system. 

 S = stiffness (ratio force to displacement) 

 St = torsional stiffness (ratio moment to angle) 

 n = frequency of free vibration 

 • ldn -ldS 



n = ~~r; s = a^; etc - 



nde S dd 



c, C, Ct, Ci, C 2 , Ci 2 = dimensionless "shape factors," i.e., con- 

 stants fixed by Poisson's ratio and the generalized shape. 



The most important results of this paper are to be found in 

 the four formulas (1), (4), (11), and (12), giving respectively the 

 frequency of a single body, the change in frequency with tem- 

 perature, the frequency of a coupled system, and the change in 

 this frequency with temperature. 



General formulas for frequency of a single body. The vibration 

 frequency for all bodies of the same generalized shape (it will be 

 recalled that this implies not only geometrical similarity but 

 also a similar distribution of density and the other properties 

 of the material) may be written 



Lip Lip y 



= JM $ (a) = Jht * M ( 



* m * m ) 



