I-Miri Yang 



sea. Therefore I am concerned about some aspects of that is in this 

 paper and how they modify what may be considered as some results of 

 my own some time ago, and therefore raise questions. For one thing, 

 this being a naval hydrodynamic symposium, there is no indication as 

 to what is unique in the paper from a hydrodynamic point of view. 

 There are walls and there is a mention by the author of the fact that 

 the added mass and damping are affected by the presence of the walls. 

 However, how did you take account of it ? What mathematical proce- 

 dures, what techniques, what approaches were used ? This is the sort 

 of information that we professionals could make some use of and would 

 like to hear about so that if we have an apposing point of view or some- 

 thing interesting to say there can be some interchange in regard to it. 



Another point is that this was applied, we are told, to a con- 

 tainer ship. Was there anything unique about the container ship ? Was 

 it a standard ship ? Was it one that also had barges perhaps ? Was it 

 an unusual form, like a Lash or a Seabee ? This makes a difference 

 in the type of ship computation per se. 



On the question of non-linearity, what kind of non-linearities 

 do we have ? I can imagine something with fenders. A fender will 

 only provide a force, and it is one-sided, when you press against it ; 

 when you go off, there is nothing. I would make an analogy with the 

 so-called linear detector in electronics, which is one-sided in its va- 

 riation. If you do that, you have a mathematical structure of what a 

 non linearity looks like. Similarly with regard to other aspects of the 

 non-linearity that comes from the mooring cable. For example, you 

 made a particular assumption in your mathematical procedure which 

 raises a very significant question in my mind. Equation 13 in the 

 paper, which you alluded to also on your slide, said that you made 

 the assumption that the Kij terms are zero. This means you are only 

 using diagonal terms in the K matrix. The implication of that is very 

 interesting. It means that you just take account of what I consider to 

 be self-mode non-linearities - that is, non-linearities in each mode 

 separately, like x , x , y , y . Moored ships certainly have inter- 

 actions of a non-linear nature because the bow and the stern when you 

 yaw together with sway have some xx y + x sine and y - x sine at 

 either end. Non-linearity reflects itself differently in different pro- 

 ducts. In fact, if you have similar mooring cables you can use the 

 fact that the cross product term is opposite sines and this will allow 

 you to get some information, something useful, and not as restricted 

 as it is here. It is a suggestion. I do not know what you have perhaps 

 done in considering that which led you to the -conclusion of a reduced 

 number of terms. 



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