502 



MR. A. E. H. LOVE ON THE SMALL FREE VIBRATIONS 



M 2 (l + o- 2 ) 

 M 2 = 7n 2 + 



(1 4- } = h -- I 



?-B.(l+..)-&\- W 



f 2V o/9 



2 " 2 * 1 -/ 



Also 



' 



', = , (J, | + ^ 



n 



', = . (J, | + -, I- 



> (5) 



According to the general principles of KIECHHOFF'S method, we may for a first 

 approximation omit the u, v, w which occur in equations (2) and (3), thus 

 re-writing : 



B./ am *\ T', 



g = < i5^(^}~ hk r + h* P p 



srG' 



a /i 



a 



a^ 

 a /i 





a m v, Kfi 



r " P ~ * 



Since we must have 



we find 



a 2 M/ 

 ^ , 



a* ' 



7> = 

 W' 



1/L\ T ' =A ^ 1/1') v = -*'. 



(8) 



Let K u Aj, 

 let K\ K 1 



I, K 2 , A 2 , T 2 be the values of K' I} X' lf T',, /c' 2 , X' 2) r' 2 before strain, and 

 K lt \\ A x = Xj, T j T z = T^ and similarly for the others, then 



I = A 2 , ! = X 2) T! = T 2 = 0. 



