This solution satisfies the governing equation. Equation 1, provided the 

 friction of water on the cable may be neglected. In Appendix A of the reference 

 report it is shown that this assumption is valid for the frequency range of interest. 



Substituting Equation 5 into Equation 2 and incorporating the boundary 

 conditions, the unknown complex constant C is determined as 



c = ^ u\{-^ +\^u\) 



(A-3) 



and hence. Equation 5 reduces to 



.^2 



U' = U'^ sec(pcos(co'y' + <p) + 1/3(11'^ toncpsinw'y' (A-4) 



where 



to' - 77 



tancp = -r^ r ^(p^y 



(A-5) 



In requiring that | U' at y' = 1 be equal to 1, Ui is determined to be 



1/2 



f\\'\2 - COS^ (60' + (p) 



^ 1^ 9 9 9 



2)3^ sin-^cpsin^co' 



^ ^^sin^co' sin^2(p 



COS (to' +(p) 



- 1 



(8) 



If the amplitude of the dynamic stress is denoted by I and a normalized stress 

 amplitude, I', is defined equal to LI/|Uq|E, the distribution of I' is given by 



r = oo' U'^ seccp sin (co' y' + (p) - i CO/S (U'^^ tancp cos to' y' (A -6) 



Hence the normalized amplitude of the maximum dynamic stress! ^JpQx '^ °^ *^^ ^°"" 



(7) 



(^max^^ = (to')^(U\)^[l + tan(p(tan^+sec^)] 



where 



.2 ... 



(U')2 = cos (to' + (p) 



2i82 sin^<psin^co' 



9 2 2 



p sin to' sin 2(p 



cos'* (to' +(p) 



1/2 



- 1 



oo' 77 



cp = arc tan — , ^ <p ^ -=^ 



(8) 

 (9) 



60 



