Page 213 - Practical Design Ships and Floating Structures

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where lack adequate land. Nowadays, the possibility of utilization of VLFS had been enhanced
gradually through recent researches and developments. A varieties of researches on response in waves
can be found (for example, Mamidipudi & Webster (1994), Hirayama & Ma (1995a), Kashiwagi &
Furukawa (1997), Ohkusu & Namba (1998)), however, most of concerns in these studies are paid on
hydro-elastic response, which is considered to be induced by first order wave forces in general. On the
other hand, as many other floating structures, wave drift forces and mooring problem is one of key
points in design. Therefore, an adequate prediction method for the wave drift force is indispensable.
However, for the reason of enormous structure size and complexity arose from the existence of elastic
deformation modes, few studies both theoretically and experimentally are available (Maeda et al
(1998)). Thus, the basic knowledge on wave drift forces as well as wind, current loads on VLFS are
considered to be insufficient from the viewpoint of establishment of the design synthesis.
In this paper, three dimensional numerical method based on direct integration of pressure was applied
to estimate the steady wave drift forces. The results have been verified by the corresponding model
experiments in wave basin using large elastic floating models, which are moored linear springs.
Through the comparisons of numerical and experimental results, the availability of so-called “Near
Field Theory” for predicting wave drift forces had been confirmed. It is shown that bending
distortional modes, which dominate the deflection of structure, can be taken into account successfully
using mode superposition approach. Furthermore, influence of flexibility on drift forces, which might
be great interest of design, is discussed through numerical and experimental results.
The different tendencies of wave drift force of two typical VLFSs, i.e. semi-submersible unit and
pontoon unit supported floating structure are discussed as well as their hydro-elastic responses. The
important factors for design, such as shape of underwater floating unit, rigidity of structure are
investigated consequently.

2 NUMERICAL PREDICTION

In order to predict the hydro-elastic response and drift force in regular waves, a widely used numerical
method, three-dimensional source method was applied. The deformations of elastic structure were
determined by modal analysis approach. By accomplishing these two analyses, hydro-elastic response
can be obtained easily by superposing the necessary modes. As for steady wave drift force, a so-called
“Near Field Theory”, which integrates the pressure of second order on wetted surface, was applied.
The fluid is assumed to be ideal fluid, the motion and wave amplitude are assumed to be small. For the
sake of simplicity, we limit the analysis to heading wave condition here.
2.1 Hydro-eimtic Response Analysis

As it is well known, fluid motion surrounding oscillating body in regular waves can be described in
forms of velocity potentials expressed as follows.
[ m 1
((4 YY 2, t) = 40 (XY YY z) + 4d (XY Y, 2) + c 4r (X, Yy ZIP, eiaY (1)
r=l
Where, 4 o ,4 d $4 I represents incident, diffracted, radiated wave respectively, p is the principal
coordinate of mode including elastic deformation, m is number of mode (m= 1-6: rigid motions, m>6:
elastic mode). For an undisturbed free surface of incident wave, we can write its potential as follows.

W, C , x denote angular frequency, amplitude and incident angle of wave respectively, d is water
depth, k is wave number which satisfies w2 = kg tanh kd .
In general, diffraction and radiation velocity potentids can be determined by solving Laplace Equation
and applying suitable boundary conditions on fiee surface, sea bottom and wetted body surface. For