Kim and Mevcier 



regular long-crested waves, such that the deck structure behaves like 

 a beam (the more general case would have to represent the deck's 

 elasticity as plate-like, or describe the details of the deck-truss 

 structural behavior). These partial differential equations are consider- 

 ably more complicated than the simpler equation (30). The deformat- 

 ion of the deck of a rectangular array of floats in regular "head" seas, 

 assuming that no hydrodynamic interaction effects occur on the vertic- 

 al forces on float elements, will be (at least in the case of linear re- 

 sponse) a traveling wave with the same frequency and celerity as the 

 incident water wave : 



z b = z o sin rf L - wt ) (31) 



**. A-,4 



£>x 4 



'■*_ -. M 



$ 



z b (32) 



2 

 or, since for water waves 2tr/\ = w /j 



>\ 



z u (33) 



.4 4 b 



ox g 



d 4 z 

 The importance of a restoring force term like EI 4 , compared to 



pgA w z , increases as the frequency increases, or^he wave length 



decreases. The design of the float -attenuator geometry is intended to 



produce vanishingly small wave-induced vertical force as frequency is 



increased. GAC structural analysts decided that the simple Eq.(30) 



is appropriate for analyses of the motions of the deck supported by a 



resiliently-connnected array of floats, such as is shown in Figure 26. 



Coefficients of the Equation and Forces for Regular Waves 



Elementary hydrodynamic theory can be applied to the estimat- 

 ion of the hydrodynamic coefficients and the wave-exciting forces for 

 the equations of motion of slender vertical floats without external ap- 

 pendages. In the present instance, it is anticipated that external ap- 

 pendages will be required to assure sufficient heave damping and 

 analyses of the hydrodynamic effects of the appendages must be ap- 

 proximate and quasi-empirical. 



The buoyant force rate has already been expressed as 

 Z z " "g A w ■ 



The vertical wave-exciting force can be expressed as 



822 



