Equations 16, 18, and 19 determine completely the amplitudes of the 

 normalized displacement and stress waves as functions of y', uj' and the two 

 parameters \i and B . 



1 ■ Summary of Formulae for the Magnitudes of the 

 Amplitudes of the Array Displacement, Maximum 

 Stress, and Stress at the Two Ends of the Cable 



Equation 19 shows that the distribution of E' along the cable is sinus- 

 oidal. Therefore, depending on the frequency and length of the cable, E' can 

 have absolute maxima and minima. These extreme values of E' , as well as 

 their locations, can be computed analytically. Denoting the magnitude of the 

 maximum of E' as lE'j^g^j^l the location(s) of this niaximum as y'ji^ax ' the mag- 

 nitudes of E' at x' = and x' = 1 as |Eq1 and ■ I E J , respectively, one can 

 show that: 



where: 



E' 



= (uj'f (Up = 



1 + tan (i (tan 'f + sec "f) 



2 U)'y' = ^ - ^, n = 1, 5, 9 



' max 2 



(20) 

 (21) 



= (UJ')^ (U.)= I 1 + 2 tan (^ cos^ t«' (tan ¥ + tanuj') (22) 



= (ti)')^ (U')^ [l + 2 tan tan ?] 



(23) 



(U'f = cos^ (m' +0) 



2 B^- sin^ sin^ m' 



P^sin^m'sin^ 2 (t . 

 cos (u)' + 0) 



(24) 



= arc tan 



< * < - 



(25) 



Y = arc tan 



- 3^ (U^)= tan - cot 2 



- - < y < - 



2 - - 2 



(26) 



15 



artbur B.ILittlc Jnt. 



S-7001-0307 



