Hello!
Thank you for your information Aina.
I used a different approach for the calculation of system movements in frequency domain.
Instead adding the linearized properties of the turbine in a diffraction/radiation hydrodynamic code, I add the hydrodynamic properties (added mass and wave damping) and mooring properties (stiffness matrix) in FAST and use the linearization process around steady-state position.
As a results, I obtained as FAST output a linearized representation of the system in term of inertia M_res, damping L_res and stiffness K_res:
M_res = System inertia + added mass
L_res = aerodynamic damping + radiation damping
K_res = K_a + K_wt + K_wp + K_h + K_m
K_wt and K_wp depend on the acceleration. Calculating this term by taking into account the whole loads on the system permit to have the right acceleration.
Using these matrices and excitation force F_ex (calculated with a diffraction/radiation code), we can calculate the RAOs of the system:
-w^2( M_res(w) + iw L_res(w) + K_res(w) ) X = F_ex(w)
w is the wave frequency. X is the vector of Platform DOFs.
I think this method has advantages. The linearized properties of the turbine (included in FAST output matrices) are calculated for each wave frequency. As in time domain calculation, aerodynamic properties will depend on wave frequency.
I compared this approach with a time domain approach. There is a very good agreement between time and frequency domain calculation, even for pitch motion.
This frequency domain approach also allows to calculate natural frequencies and modes of motion of the system by resolving equation for the free motions.
I hope this information may be useful. I may send more information by email if someone is interested.
With best regards
Maxime PHILIPPE
Ph.D candidate
Laboratoire de Mécanique des Fluides
Ecole Centrale Nantes
Nantes, France