The boundary conditions at the upper end of the cable is the specification that 

 u at x' = 0. The boundary condition at the load, when x = L, is given by 



ao ^^ 2D 



lf = ° 



(A-2) 



where M = dynamic mass of the array 



C_ = drag coefficient of the array 

 A = horizontal cross section of the load 

 By defining the parameters 



M = 



P,SL 



M, 



B = 



CpPA 

 2M_ 



(4b, f) 



Equation A-2 may be reduced to 



(St')2 



+ 1^ 



5u 

 Sx' 



+ B 



du 



at' 



at' 



= 



(2) 



atx'= 1.0. 



The difficulty of applying this boundary condition. Equation A-2, arises from 

 the nonlinear term B | au/at' | (au/at'), which represents the drag on the load. To 

 avoid the complexities arising from this nonlinear term, an approximation was made 

 in the reference report by replacing the |au/at'| term by (8/3 7t)ujU], where U] is 

 the amplitude of the load displacement, which Is assumed to be sinusoidal. This 

 selection results in the same energy dissipation when u is sinusoidal in the third term 

 of Equation 2. It is demonstrated in the report that this approximation leads to 

 errors on the order of 20% in the drag term. 



Defining a normalized displacement amplitude U' equal to U divided by | Uq| 

 and noting that U'l is the value of U' at the load, a solution for U' as a function of 

 x' is given by 



U' 



U'lCosCO'y' + Csinco'y' 



/here y' = 1 - x' and 



coL 



(5) 



(6b) 



59 



