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BELL SYSTEM TECHNICAL JOURNAL 



set to zero at the faces of the plate; i.e. at j = ±- . Three equations, after 

 simplifying, result. 



For Fj; = Oat 3/ = ±- 



Ui aBik" + ^1 + in) sm{i^ + A( 



Isin^:^] 



+ t/o \a(1 sin A ^ - Uz \a (/;' + in) sin /"s ^ = 



(7.47) 



ForXj, = Oat y = ±- 



f/i [2^1 cos (i y + U2 [2C2 cos ^2 y 



+ Uz\C,- 



['-'^'][»'-a-» 



(7.48) 



For F^ = at 3/ = ±- 



f/i r2rim cos ^1 y + C/2 ["(/sw - ^y' (f^ + Z;')^ cos A ^ j 



+ t/3 ["(/"aw - y^ (/c' + w )^ cos ^3^=0 



(7.49) 



In order for these three equations to be satisfied simultaneously a neces- 

 sary condition is that the third order determinant formed by the coefficients 

 of the t/'s vanish. That is, 



UaB{k' + /? + m') + A(l) sin (^ ^] ^A(l sin (^ \ 



A (k^ 4- in) sin {3 - 



llCx cos ^1 ^1 





2^2 CCS/'2^ 

 )cOs/3^] 



[2rxm cos A^] [(^2^ - ^yj (^^ + A'^)) cos ^2 2] 

 ( 4w - '^^ (^"^ + Pi')] cos /"a - 



= (7.50) 



