Vessel Motions – Superposition of Harmonics |
 
|
Vessel Motions – Superposition of Harmonics |
|
The high frequency response 
of the vessel reference point in local degree of freedom i to a Dean’s Stream Function wave when you nominate the Superposition of Harmonics option is defined by:
(1)
where:
•
is the vessel RAO in degree of freedom i, which is a function of wave heading 
and wave frequency 
•
is the vessel phase angle in degree of freedom i, which is also a function of 
and 
•f is the surface elevation function as defined in the Deans Stream Wave - Theory (Eq.3).
Remaining symbols are as previously. With this option, the vessel response is a summation of N components, which correspond to the “components” in the expression for water surface elevation in the Deans Stream Wave - Theory (Eq.2). RAO values and phase angles corresponding to each component in the Deans Stream Wave - Theory (Eq.2) are extracted from the user-specified data in the usual way, and the vessel response is found by summing over the N terms in a similar manner as would be used in a random sea. Obviously for this exercise to be meaningful RAOs and phase angles must be defined over the full range of circular frequencies from 
to 
.