Page 52 - Marine Structural Design

Chapter 2 Wave Loah for Ship Design and Classijkation 29

The first part of the right hand side in Eq. (2.23) refers to the hydrodynamic forces acting on
the ship:
( 2)
F,(x,t)=-- D m(x,v)- -N(x.B)- D17 (2.26)
Dt Dt
where,
rn = Added mass (due to the hydrodynamic load) per unit length
N = Damping force per unit length
D/Dt = Total derivative with respect to time t
In recent years, the diftiaction and radiation theories based on panel methods became widely
accepted (Faltinsen, 1990).
More recent advanced methods include Mly nonlinear timedomain approaches. Cao et a1
(1991) used a desigularized method in which the source panels are located outside the fluid
domain and thus the kernel in the governing integral equation is desigularized. The
desingularized method was developed for more general boundary value problems of potential
flows and was used in the time-domain computations of fully nonlinear waves. Jensen et a1
(2000) gave a detailed discussion of the different theories and comparisons with experiments
on extreme hull girder loads. Beck and Reed (2001) gave a precise account of all fundamental
theoretical developments in the field of sea-keeping over the past 50 years as well as the
computational methods that currently in use.
The large amplitude motion programs FXEDYN (De Kat and Pauling, 1989) and LAMP (Lin
et al, 1997) may be used to calculate the extreme loads, capsizing, habitability and crew
effectiveness. Other popular hydrodynamics codes include WAMIT (WAMIT, 1999), SWAN
(Sclavounos et a1 , 1997).

2.3.3 Structural Response
Once the forces (or loads) acting on a ship are calculated, the hull girder response of the ship
may be determined. In most cases, the hull girder analysis means calculating the longitudinal
bending moment of the ship. It is performed by assuming the hull is rigid, e.g. no deformation.
However, there are a number of cases in which the ship needs to be considered as a flexible
beam, thus resulting in a more complicated solution that must include a hydroelastic analysis
of wave-induced loads. Examples of cases when the ship is assumed flexible are:
(1) When the ship’s natural vibration is low enough to cause significant vibrations during its
operational life.
(2) When the ship’s response to slamming and green water on deck needs to be investigated
The governing differential equation for the vertical deflection of a flexible beam subjected to a
dynamic distributed load F(x,t) is:

a4v a2v a4v
-
-
EI--+ ms --msr2 - F(xJ) (2.27)
at2&2
ax4 at2
where,
E = Young’s Modulus
Z = Moment of inertia for vertical bending