Analyses of Multiple-Float-Supported Platforms in Waves 



*L 



kz 

 e 

 e 



Z f f = PgfS(O) - P gKJ (l-e kZ )-^-dz - Z^-^-Em'o; f 



Hydrostatic ,,„ ljL1 ,,„' ' . Damping Added mass 



J Smith Correction to 



Froude -Krylov 

 where 



(34) 



£JT • 



KJ. 



S = sectional area of body 



k = wave number =« / g = 2 7r/\ 



X = wave length 



+x Z. = damping coefficient 



f = wave elevation 



K - wave amplitude 

 o 



f = wave motion evaluated at 

 depth corresponding to as- 

 sumed damping source 



' = element of effective added 

 mass in vertical direction 



m 



z = effective depth for evaluating 

 wave acceleration for element 

 of added mass 



The Froude-Krylov force corresponds to that predicted by slender 

 body theory and is the same as predicted by assuming that the presence 

 of the body does not influence the wave's pressure field. For finite 

 draft, T , the Froude-Krylov force decreases with increasing wave 

 frequency (because of more rapid attenuation of wave pressure with 

 depth) and, if the attenuator is shaped as in the sketch, may become 

 opposed in sense to the wave elevation for sufficiently high frequencies. 



The response of slender spar buoys to waves has oeen studied 

 by Newman [36j , who performed a detailed slender-body analysis and 

 by Rudnick [3 7] , who derived equations similar to Newman's [36J on 

 the basis of a more elementary analysis, and who compared results 

 of calculations with field measurements of the motions of the Flip 

 platform. Newman notes that the slender -body theory applied to floats 

 in waves loase its applicability at higher values of slenderness ratio 

 than is the experience for aerodynamic analyses. Adee and Bai [38j 

 have conducted experiments with cylindrical models having either flat 

 or conical bottom ends and various draft-to-diameter ratios. They 

 find that it is important to account for added mass effects even for 

 quite slender floats. However, while they include added mass effects 



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