Page 223 - Practical Design Ships and Floating Structures

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particular very large floating structure to the dynamic loads. The states of which mooring clearance
and the ultimate strength mooring fender exists are numerically calculated, it is seen that the structure
rigidity has a substantial effect on the result of VLFS mode and the eigen frequency, as well as the
difference response due to the condition of incident wave. It is concluded that design should be
considered with respect to the overall structure dynamic characteristics of the VLFS

2 BASICSTUDY
2.1 Outline of WFS Under Trial Design
In this study, we deal with a very large floating structure (VLFS) under trial design, which is
developed for the usage of a floating airport, for simplicity, we model the main body of the structure as
beam supported with many dolphins shown in Fig. 1 and indicate its main parameters in Table 1.

The dolphins attached to the fender as the shock-absorbing parts at the top end and driven into the base
rock at the bottom end are also model as spring elements as shown in Fig. 1. The numerical data for
foundation spring and column elements are calculated out using a three-dimension finite element
method and based on the experiment report” as shown in Table2.

2.2 Eigen Frequency Characteristics

The solution of the real eigenvalue problem is very important for the following time history simulation
analysis which is numerically difficult and time consuming, therefore, we investigate the eigen
characteristics and normal modes of the VLFS by using both theoretical analysis and finite element
methods at first.
For simplicity, we shall model the main structure as Timoshenko’s beam on an elastic foundation, we
can obtain the control elastically deflecting Eq. 1 as following.

a4v a2v E a4v p2z p I a2v EI d2v
+
-
EZ - pA - pI(1 + -)- +--+kc(v+----
ax4 at2 k’G at2&’ R’G at‘ R‘GA at2 L’GA 2) = (1)
where, v: elastic deflection, p~ : linear density of main structure, bending rigidity, k’GA: effective
shearing rigidity, k, : mooring rigidity.
By introducing the following constant variables into Eq. 1, we can re-write it as following.
-
a4v a4v k4 a2v za4v a2v a2v
--(a2+f12)-+g-+a fl -+k;v+a fl wo --y 7=0
ax4 at2&= at2 at at2 ax (2)

constant are the component of shearing rigidity and rotating inertia moment respectively, 0 is
horizontal circular frequency when treating structure as rigid body, Y is the relationship between
inertia and rigidity, andk. indicates the relationship between bending rigidity and mooring rigidity.