Page 255 - Practical Design Ships and Floating Structures

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of VLFS on the irregular waves. The results in the time domain are compared with those in the
frequency domain.

2 FREQUENCY DOMAIN ANALYSIS

The Cartisian coordinates are defined with z=O as the plane of undisturbed free surface and z=-h as the
horizontal sea bottom(Fig. 1). Velocity potential @ are expressed as follows.
3N
D = im[g('I + 'd) + c wj'j le'"
j=l
where, N=NxxNy/4

Where & is the amplitude of incident wave, wj complex amplitude of motion. Suffix d represents
quantities related to the diffraction potential and suffixj represents heave, roll and pitch mode. The
segmentation of panels are made such that the plate is subdivided into Nx in the x-axis and Ny in the
y-axis and is composed of the group of N bodies. In the definition of radiation indices, the unit
vertical motion of each body is described for representing elastic deformation due to radiation
problems and one body is composed of four neighboring panels(Fig. 2).

" . ~
Wave
Direction + drn ; >x
1240m
VLFS
, .... * .,..
~ ....................................................... .... ................................................. 3
1,200m

Figure 1 : Cartesian coordinate system
As linear potential theory is assumed, the velocity potential must satisfy the Laplace equation, linear
free surface boundary condition, sea bottom boundary condition and radiation condition at far field.
The body boundary conditions for the radiation and diffraction problem are given as follows.

=
- -- on the body (3)
"I
dn dn
where, n, : the direction cosine in the heave mode of motion.
The incident wave potential in Eqn. (4) satisfies the relation Eqn. (5).