SUMMARY OF THE RESPONSE OF MOORED FLOATING PLATFORMS TO OCEAN WAVES 



By 

 Dr. J. R. Paulling 



I appreciate being given the opportunity to participate in the 

 Mooring Dynamics Seminar on January 10-11 and feel that it was an effec- 

 tive and worthwhile meeting. I believe that you were able to bring 

 together an enthusiastic group of people, representing all of the scien- 

 tific and engineering disciplines which are of importance in dealing 

 with mooring problems, and all participants seemed to have some signif- 

 icant contributions to the discussions which took place. One feature 

 which made the meeting especially worthwhile was the small size of the 

 group, which eliminated any feeling of formality and made possible some 

 very spontaneous and stimulating discussions. 



In reviewing my notes on the discussions, there are two points 

 which I think should be considered in directing your future work, and I 

 have outlined them below. 



1. The methodology for solving the response of a moored ship involves 

 the simultaneous solution for linear and nonlinear motion effects. This 

 is because the wave frequency ship motions are reasonably well predicted 

 by linear methods (e.g., strip theory), while the slow drift forces, 

 which are important to the mooring dynamics, depend in part on two 

 nonlinear effects: the wave reflection, which is proportional to the 

 square of the wave amplitude, and the nonlinear interaction between the 

 waves and ship motion, which is neglected in strip theory. 



The simultaneous solution might be approached in either of two 

 ways, and the optimum is not completely clear at this point. The first 

 is to use a sort of "brute force" direct numerical integration of the 

 complete equations of motion, which include both the linear and nonlinear 

 effects. The potential drawbacks to this procedure are the computer 

 time requirements for direct integration and, second, the complication 

 of including the frequency-dependent hydrodynamic forces on the ship. 

 The latter can be overcome by a convolution integral technique, and has 

 been applied to ship steering problems by a student of mine, Dr. Leo 

 Perez. The second procedure would involve several steps as follows: 



a. Solve for the linear response of the moored ship. 



b. Compute the nonlinear slow drift forces using this response 

 combined with the assumed wave spectrum. 



c. Solve for the nonlinear response of the moored ship to the 

 slow drift forces of b. 



d. If the slow drift large amplitude motion results in sufficient 

 change in the mooring configuration to appreciably affect the 

 linear response, repeat steps a-c. Several iterations may be 

 required before the process converges. 



This procedure has the possible advantage of breaking the total problem 

 down into two somewhat simpler ones which are then solved separately. 1 

 do not know of its having been tried in a similar context, and it is not 

 certain that convergence will be assured. 



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