[- (M + M, ()) anne iwy () + pgAl a BA) 
where the heave as a function of time is equal to the real part of 
Ze - The other terms are 
M - mass of platform 
M, () - added mass factor 
y(w) - damping due to wave making 
o - density of fluid 
g - acceleration of gravity 
A - waterplane area of platform 
w - frequency of waves (radians/sec) 
Re complex amplitude of heave 
Z 
AO) - force exerted on platform due to waves 
Simple division by the bracket on the left side of the equation gives 
an immediate solution. However, there are still complications. Exact 
expressions for the added mass, damping, and waves forces are not known. 
Approximate formuli for these quantities were obtained by use of Grim's 
(1959) coefficients. These coefficients were generated for use in the 
strip method for analyzing ship motions, and their use in the present 
case is justified primarily for purposes of expediency. 
In the strip theory, the floating structure is mathematically 
divided into thin transverse strips. The wave forces, added mass, and 
damping coefficients are calculated for each strip on the assumption 
that the presence of one strip does not influence the waves incident on 
other strips. The total effect is then obtained by integrating over 
all the strips. In general, the coefficients generated by Grim depend 
on the wave frequency as well as the beam, draft and section fullness 
of the ship. Kaplan and Putz (1962) using Grim's formulation, obtain 
the following formuli for the forces on a thin section of the structure: 
aM, (€) a6 onB” (C) ding 
8 
pw G)° ac 
2 
dy (G)) = C, 
n I B D 
dF (6) = dE, (G) + dF (C) + dF (C) 
where 
ar, (C) = Se hs BO) & eam) 6 ae 
8 
