Kim and Mercier 



For example, if a probability of being exceeded is 0.1, the expression 

 implies that one platform in ten floating in the same area or statistical 

 environment may experience a larger response than the estimated ex- 

 treme value (x) during the specified duration. 



Because this type of response information is of interest for 

 certain investigations the second moment of the response spectra, E. , 

 have been calculated according to Equation (10) and included in Tables 

 5. It may be appropriate to note that a recent study by Dalzell [22] of 

 the statistics of responses of systems with non-linearities suggests 

 that applications which assume the Rayleigh distribution and involve 

 order statistics and/or the estimation of extremes tend to over-predict. 

 Since most platforms are subject to some extent of non-linear damping, 

 at least for extreme sea states, Dalzell' s observations should be borne 

 in mind. 



SOME PROBLEMS OF THE HYDRODYNAMIC INTERACTION 

 BETWEEN TWO FLOATING BODIES IN BEAM SEAS 



BACKGROUND 



Ohsusu [23,24] has theoretically evaluated the hydrodynamic 

 forces and moments on two or more cylinders heaving, swaying and 

 rolling on a calm water surface. Ohkusu and Takaki [25] have applied 

 these analyses to evaluate the motions of multi-hull ships in waves. 

 Wang and Wahab [26] have also studied the hydrodynamic forces on 

 twin heaving cylinders on a calm water surface. 



These investigators used the method of multipole expansion to 

 determine the unknown velocity potential. In these analyses, the in- 

 dividual section must be symmetrical about its own vertical midplane 

 and the two cylinders must be identical. 



Lee, Jones and Bedel [2 7] have reported theoretical and ex- 

 perimental evaluations of the hydrodynamic forces on twin heaving 

 cylinders on a calm water surface. Their theoretical analysis follow- 

 ed the method of source distribution over the immersed contours [28] 

 of the cylinders. Consequently, cylinders of arbitrary cross-section, 

 not necessarily symmetric about their vertical midplanes can be dealt 

 with. This investigation also assumed the two cylinders to be sym- 

 metrically disposed with respect to each other. 



All the above investigations [23-2 7] of multihull cylinders as- 

 sumed that the cylinders are rigidly connected. 



806 



