Page 70 - Marine Structural Design

46 Part I Structural Design Principh

use perturbation analysis with the wave amplitude as a small parameter. The non-linear
problem is solved in second-order (Faltinsen, 1990).
In addition to the boundary element methods, finite element methods or hybrid (BEM & FEM)
methods are available to develop commercial codes for a body of general geometry's. Other
special simplified methods have also been mathematically developed for specific geometries
that are much more efficient. When viscous forces become important, a hybrid difhction and
Morison drag method is required in which the drag force calculation based on the undisturbed
flow but a more elaborate approach is applied to account for the change in flow velocity due to
diffraction.
In very deep seas various higher order wave loading effects also become very important
(CMPT, 1998):
Higher order potential flow and drag forces coupled with highly non-sinusoidal waves lead
to ringing
Impact of parts of the structure with water surface leads to bottom slamming and run up
(on near vertical surfaces). The duration of slamming pressure at a specific location is of
the order of milliseconds and the location of the peak pressure moves with time.
Bhattacharyya( 1978) gives a comprehensive and easy to follow discussion of the wave loads,
deck wetness and slamming, as well as the influence of slamming on the hull girder bending
moment.

3.3.4 Floating Structure Dynamics
Dynamic response of an offshore structure includes the sea-keeping motion of the vessel in
waves, the vibration of the structure, and the response of the moored systems. The response of
an offshore structure may be categorized by frequency-content as below:
Wave-frequency response: response with period in the range of 5 - 15 seconds. This is
the ordinary see-keeping motion of a vessel. It may be calculated using the firs-order
motion theory.
Slowly-varying response: response with period in the range of 100 - 200 seconds. This is
the slow drift motion of a vessel with its moorings. The slowly-varying response is of
equal importance as the linear first-order motions in design of mooring and riser systems.
Wind can also result in slowly-varying oscillations of marine structures with high natural
periods. This is caused by wind gusts with significant energy at periods of the order of
magnitude of a minute. Figure 3.5 shows wave frequency and slow-drift constituents for a
floating system.
High-frequency response: response with period substantially below the wave period. For
ocean-going ships, high frequency springing forces arise producing a high-frequency
structural vibration that is termed whipping (Bhattacharyya,l978). Owing to the high axial
stiffness of the tethers, TLPs have natural periods of 2 to 4 seconds in heave, roll and pitch.
Springing is a kind of resonance response to a harmonic oscillation (CMPT, 1998).
Impulsive response: Slamming occurs on the ship/platform bottoms when impulse loads
with high-pressure peaks are applied as a result of impact between a body and water.
Ringing of TLP tethers is a kind of transient response to an impulsive load. The high-
frequency response and impulsive response cannot be considered independently of the
structural response. Hydroelasticity is an important subject.