Page 219 - Dynamic Loading and Design of Structures

Page 192

It is noted that the diffraction effects will significantly reduce CM when waves with a period
of, say, 5 sec act upon columns with a diameter that exceeds 8 m. This issue is important
when the structure has natural periods around 5 sec.
Analytical solutions to several other cases of simple geometry for offshore structures can be
developed (see e.g. Gran, 1992). These generally require that the member be far removed
from a boundary, particularly the free surface. Some of these members include spheres,
horizontal cylinders, bottom seated hemispheres and bottom seated half-cylinders. For more
complex cases numerical methods have been proposed to obtain wave diffraction solutions.
These methods include boundary element, finite fluid element, conformal mapping, and
hybrid techniques. The solutions have received many experimental verifications and practical
applications (see e.g. Clauss et al., 1991, and Faltinsen, 1990).
Wave diffraction solutions do not include viscous actions. When body members are
relatively slender and have sharp edges, viscous effects may be important and should be
added to the diffraction forces determined.
Wave loads on structures composed of large volume parts and slender members may be
computed by a combination of wave diffraction theory and Morison’s equation. Parts of the
structure may be modelled both by boundary elements to represent the potential
hydrodynamic loads and beams to represent the viscous drag loads. The modifications of
velocities and accelerations as well as surface elevation (wave enhancement) due to the large
volume parts should, however, be accounted for when using Morison’s equation. This
situation may arise in connection with caissons of gravity structures, strong interaction
between large columns, non-vertical sides near the water plane and other features. The results
from boundary element methods should be carefully checked for surface-piercing bodies to
ensure that irregular frequencies are avoided. Moreover, estimates of loads for novel
structural shapes need to be checked by model tests. Model tests have also been carried out
systematically to establish Morison-type formulation for inertia forces on gravity structures
(see e.g. Moan et al. 1976).

5.3.4 Effect of motions

As mentioned above, when the structure moves, as a result of excitation forces, inertia (added
mass) and potential damping forces are generated. If the structure moves, the total inertia
force acting on a slender member of the structure, may then be established as the same FK
force as that acting on a fixed structure, together with the added mass force associated with
the relative acceleration between fluid and structure. The drag force may be established by
replacing the particle velocity in eqn (5.28) with the relative velocity. Hence, the force normal
to the axis of the member may be written as

(5.31)

Equation (5.31) is particularly relevant in connection with analysis of motions of