Analyses of Multiple-Float-Supported Platforms in Waves 



of configuration. Thus, if 3" (u>) is a non-dimensional ratio of res- 

 ponse, x , to wave elevation, J" , a non-dimensional variance may be 

 obtained as 9 , 



/33.56\/ ^ l \ 



2x0.0081 \£4g 2 A H i/ 3 ' 



E 



,2/3 



- f\a x W\ 



dof 



7) 



where the spectral formulation with only significant wave height being 

 available was chosen so that only one parameter ( V / /H.. , ) would 

 describe the relative intensity of the sea state. 



Since wave elevation has dimensions of length, the response it- 

 self must have the same dimensions. This is, of course, the typical 

 case for heave or surge but other examples of non-dimensional res- 

 ponse are : 



A 



M 



6V 



1/3 



A V 



1/3 



for pitch angle 

 for acceleration 



for relative motion 



r b for relative velocity 



M 



pgvr 



for bending moment 



a =——- for heave 



z i 



(8a) 

 (8b) 



(8c) 



(8d) 

 (8e) 

 (8f) 



and so forth. 



The dimensionless presentation of spectral response was, to 

 the authors knowledge, first introduced by Bennet [l8J in 1966, who 

 retained the two parameter (significant height and period) description 

 of the irregular seas. This very useful form of presentation has been 

 adopted by Lindgren and Williams [l9j , among others, and deserves 

 wider application. Fridsma [20] has exploited the useful scaling char- 

 acteristics of the ITTC (Pierson-Moskowitz) spectra to present dimen- 

 sionless results of motion and acceleration measurements carried out 

 with planing model hulls in waves whose spectra corresponds with the 

 ITTC recommendation. Thus, information for these highly non-linear 

 responses can be given for craft of various sizes in realistic irregul- 

 ar seas. 



803 



