Kaplan 



motion in beam seas was set up on the analog computer, with the 

 input wave force excitation assumed to be proportional to the wave 

 record, and solutions obtained for z(t), the heave motion as a 

 function of time, and also for [z(t) - T|(t)] , the relative heave 

 motion. 



At the same tinne another equation was programmed on this 

 analog computer representing the uncoupled sway motion of the 

 moored barge, viz. 



(m + Ag/y + NyY + kyy = Ygj^Ct) (137) 



where Yex(t) is the wave exciting force. This exciting force was 

 simiulated to represent the linear wave-induced force and then the 

 nonlinear drift force, with separate solutions obtained for each 

 excitation above in order to illustrate the different output results. 

 The linear wave excitation force was represented as proportional 

 to 'r\it), after a 90° phase shift over the pertinent wave bandwidth, 

 which is an adequate approximation. The nonlinear drift force was 

 represented by 



Yrfrift = PgLA,^{z - Ti}^ (138) 



where the { } symbol represents the envelope operation, and a 

 constant value is assumed for A^. The envelope of a time-varying 

 function is obtained by rectifying the signal (i.e. an absolute value 

 circuit), followed by a low pass filter. 



The results of this simulation study are shown in Fig, 15 

 for the case of linear wave force excitation and in Fig. 16 for the 

 drift force input. The time histories of the surface wave motion, 

 sway motion output, and input exciting force are shown in each 

 figure. The linear wave force response is seen in Fig. 15 to be 

 generally oscillatory, of the same general frequency content as the 

 wave input, and with an amplitude of the same order as the wave. 

 The input excitation force has somewhat higher frequency content 

 (since it is proportional to ii) and it reaches amplitudes of 4 X 10 lb, 



The sway motion in Fig. 16, due to the nonlinear drift force 

 input, has an entirely different character than the surface wave 

 motion or the wave-induced sway miotion shown in Fig. 15. It is a 

 long period, almost regular response at the natural period of sway 

 for the moored ship, viz. 64 sec. (see Table 1). The input force 

 that caused this response is also shown in Fig. 16, as derived 

 according to Eq. (138) and it can be seen to be a slowly varying 

 function of tinne, reaching a maximum value of about 50,000 lb and 

 causing a response reading up to 15 ft in amplitude. Thus the 

 characteristics of the slowly varying nonlinear force, of much 



1074 



