Page 247 - Practical Design Ships and Floating Structures

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the pressure distribution method is applied to the zero draft assumption. The effectiveness of the
shallow draft assumption is compared mainly on the elastic deformation and the steady wave drift
force. The steady wave drift force is calculated by the momentum theory.
Several numerical procedures have been proposed and developed on hydroelastic responses of a
pontoon type floating structure with a finite draft. Those procedures may take much computational
time in the relatively high frequency range. Then zero draft assumption has been introduced in order to
save computational time. (See, Maeda et al. (1996), Kashiwagi (1998), Ohmatsu (1998) and Kim et al.
(1998) ) The zero draft assumption has been partially verified by model tank tests, while the model
tests may have some uncertainty and may not correspond to the full scale wave frequency range. The
application area of the zero draft assumption is still not clear yet. Kim et al. (2000) verified about this
problem, however, there are a few examinations on the zero draft assumption related to an analysis of a
very large floating structure. In addition, few researchers verify the effectiveness of the assumption on
wave drifting forces.
Figure 1. In addition, velocity potentials @, pressures P ex
2 THEORY

It is assumed that the fluid is ideal fluid. The hydrodynamic forces are calculated by the linear
potential theory. However the second order wave
excitations are considered by the momentum theory
using the linear velocity potentials. The coordinate
system is the right hand Cartesian and the z-axis is
positive upward. The coordiiate system is illustrated in

and vertical displacement 7 of a free surface or the
structure are defined. Two methods are applied to the
hydroelasticity analysis for the pontoon type very large
floating structure. One is the three-dimensional singular I
distribution method for the analysis of finite draft bodies.
Another one is the pressure distribution method for the
analysis of zero-draft bodies. Figure 1: Coordinate system
2.1 Theoryfor afinite drap body

The 3-D singularity distribution method (3-D SDM) is used in the calculation in which the effect of the
body's draft is considered. It is very general method for an analysis of hydrodynamic forces on
offshore structure with arbitrary shapes. The authors modified our program code to calculate the elastic
floating structure. The method for an analysis of the elastic motions is same as Nagata et al. (1997).
A theory to analyze the wave drifting force which is called as the second-order wave excitation
generally is explained here. The momentum theory (far field theory) is applied.
The velocity potential 4 in the fluid field at an arbitrary point is expressed as follows:
-
a
ah
Y, X; X' ,v', z'b ,
&(.I Y, 2) = - Jl(x h ~)G(x, (1)
SH
where G is Green's function. When a distance between the source and observation points becomes
'
infinity, Green's functions (in this study) are:
_.
ti=-- i
cosh k(z + h)cosh k(z'+h)
h+-
k2 - K2
i
G = - K exp k(z + z') (3)
2