Page 249 - Practical Design Ships and Floating Structures

224

and, 'A' is the total of Kochin function:

Here, qn. is the first-order principal coordinate of r-th rigid and elastic mode. HD is the Kochin
function corresponds to the diffraction wave. Considering the second term in the right side of eq.( 15),
wave drift forces can be calculated even though the floating structure behaves an elastic motion.

3 RESULTS OF NUMERICAL CALCULATION

The corresponding model for the numerical calculations is illustrated in Figure 2. The model has
lOOOm in length, 250m in width. The water depth is 1OOm.
Variation of the draft is 2m, 5m and 8m for the finite draft cases, and the mass of the model
corresponds to 2m, 5m to 8m equivalent draft, respectively. There is another case in which the mass
distribution varies from 2m, 5m to 8m equivalent draft with the constant.
In the calculation due to the shallow draft assumption, the draft is zero, but the mass is considered in
the elastic motion equations. The corresponding mass is the one for the equivalent drafl of 2m, 5m and
8m.
The calculation results are shown in Figures. 3 to 12. In the figures, number of do, d2, d5 and d8 stand
for the draft on the hydrodynamic computational calculation. And m2, m5 and m8 mean the equivalent
draft which corresponds to the distributed mass, i.e. m2 denotes the corresponding mass to the 2m
equivalent draft. Position of the calculation of the vertical displacement is point 1 in Figure 2.
Figures 3 to 7 show the results of the vertical displacement at Point 1 in waves with 0 or 60 degrees of
incoming wave angle. Horizontal axis of following figures is a circular frequency a, which corresponds
to full scale wave condition. The response characteristics differ from each other in high frequency
ranges because of the difference of the distributed mass. The equivalent draft for the distributed mass
is as same as the corresponding draft itself in Figure 3. The effect of the zero draft assumption can be
examined in Figures 4 to 7. The effect of the draft is smaller than that of the mass. The results due to
the zero-draft theory agree with the finite draft one quantitatively and qualitatively.
Figures 8 to 10 show the steady wave drifting forces of surge or sway on the model. The elastic motion
is not considered in the results of Figures 9 and 10. The results of the zero draft theory is very good
agreement with that of the draft of 5m and 8m. The results of Figures 11 and 12 include the effect of
the elastic motion of the model in 60 degrees wave. The wave drift force of surge becomes negative
value in an oblique wave. The results of the zero-draft theory do not agree with the results of 2m in
draft. The authors think that the cause is accuracy of the numerical calculation, i.e. the computation is
severe in case of very shallow draft condition in the 3-D SDM.
4 CONCLUSIONS

Practically speaking we can conclude that the zero draft assumption(shal1ow draft assumption) is
applicable to the calculation for hydroelastic behavior of a VLFS. The detail is as follows:
1) The zero draft assumption is very effective because the elastic response is mainly based on the