Hello Dr. Jonkman,
I am trying to calculate the natural frequencies of the surge, sway, heave, roll, and pitch of the OC4 platform using the data in the ‘Definition of the Semisubmersible Floating System for Phase II of OC4.
- The stiffness Kp of the platform is composed of the mooring stiffness (Cm(1,1)=Cm(2,2)=7.08e4 N/m, Cm(3,3)=1.91e4 N/m, Cm(4,4)=Cm(5,5)=8.73e7 Nm/rad, from Eq. (5-15)) and hydrostatic stiffness (Ch(1,1)=Ch(2,2)=0, Ch(3,3)=3.836e6 N/m, Ch(4,4)=Ch(5,5)=-3.776e8 Nm/rad, from Eq.(4-3)).
- The mass of the platform is mt(1,1)=mt(2,2)=mt(3,3)=1.3473e 7 kg in the surge and sway directions, and the roll and pitch inertia is mt(4,4) =mt(5,5)=6.827e9 kg-m2 for the pitch and roll motions.
- The added mass A(1,1)= A(2,2)=6.49e6 kg, A(3,3)=14.7e6 kg, A(4,4)= A(5,5)=7.21e9 kg.
The angular natural frequency at the individual direction is wi=sqrt((Cm+Ch/(mt+A)) and is fi=wi/(2*pi) in Hz.
The calculated frequencies in Hz are
surge 0.0095; [0.0093]
sway 0.0095; [0.0088]
heave 0.0589; [0.0578]
roll 0.0229; [0.0375]
pitch 0.0229; [0.0373]
where the second column shows the reference results by Alexander Jeta which are very closed to these in the Fig3 of ‘Offshore Code Comparison Collaboration Continuation Within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible Wind System’.
It shows the results in the surge, sway, and heave directions are acceptable, while, the roll and pitch motion frequencies are incorrect. Do you have any idea and suggestion about this? Thanks in advance.