Kim and Meroier 



Spectral Response 



The statistics of the heave motion response may be derived 

 for slender vertical floats using the transfer functions and the (di- 

 mensionless form of the) Pierson-Moskowitz wave spectrum, as was 

 done in the first part of the paper for three- and four- float platforms. 

 The significant dimension for use in non-dimensionalizing will be the 

 draft for this case, instead of V ' . 



Some results showing the effect on "significant heave motion", 

 z-^ /o/T , of R a /R , are given in Figure 31, with other particulars, 

 the same as for Figure 27 . The influence of L a /T Q n the significant 

 heave is shown in Figure 32 for the same cases as are considered in 

 Figure 28. The effect of T/R on the statistical responses is small, 

 as might be expected from the results for forces shown in Figure 29 - 

 at least for floats which are sufficiently slender. 



According to Figures 31 and 32, the "best" float shape is 

 evidently a function of the design sea state or significant height : 

 slender floats with displacement relatively uniformly distributed be- 

 ing better for mild sea conditions while higher values of R a /R Q with 

 the displacement concentrated near the bottom are better for more 

 severe seas. An irregularity, or "bump", is discernible in some of 

 the curves for values of H, /„/T at which an increase of sea state 

 introduces a large increment of wave energy at the resonant frequency 

 of the float. 



It is interesting to note that the dependence on significant wave 

 height of other heave-related spectral response characteristics may 

 differ from that of heave. Figure 33 shows significant values of heave 

 motion, vertical acceleration, and deck curvature ^ £ , for a partic- 

 ular float having R a /R Q = 1.8 , L & /T = 0.5 , and*' T/R q = 30. Since 

 the transfer functions for acceleration and deck curvature depend on 

 frequency in a different way than does heave, weighing high frequency 

 more heavily, while attenuating low-frequency input, higher sea states 

 do not produce as much increase of response as for heave. This is 

 because an increase of sea state (according to the Pierson-Moskowitz 

 spectra) adds significant energy in the low frequency range but not 

 much at higher frequencies. For the case presented, the deck curvat- 

 ures (and therefore the deck stresses) are very nearly proportional to 

 the significant wave height, since 



T 1— / (H . /T)w0.3 over the range of H , /T values 



presented. 



828 



