Dear all,
I had extracted the mooring stiffness matrix from MAP++ using pymap, I have some doubts in it.
[1] I want to know whether there is any relation exist between the elements of stiffness matrix or not?
[2] Is there some existing theoretical form of stiffness matrix just like the mass matrix?
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
I’m not sure what kind of “relationships” you have in mind, but the mooring stiffness stiffness matrix depends on the line types (catenary, taut, or semi-taut) and geometry of the mooring lines and their interconnections.
Best regards,
Dear @Jason.Jonkman ,
Actually when I am changing any line property such as EA etc. the whole mooring stiffness matrix changes. I want to check how the values are changing as I am not able to identify any particular pattern between the former and later matrices.
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
That is likely because the mooring system stiffness depends not only on the elastic (EA) stiffness, but also the geometric stiffness associated with the line type and line geometry.
Best regards,
Dear @ Jason.Jonkman,
I am attempting to derive the structural dynamic model for a floating wind turbine, and I have found the form of the stiffness matrix for the linear mooring system in OC3 Hywind report..my model’s coordinate system origin resides at the platform center of mass whereas OpenFAST uses the still water level (SWL) origin. Could you advise how to derive the mooring restoring force matrix for this scenario—specifically, whether it can be obtained via transformation of Eqs. 5-2/5-3?
I have referenced several literatures and attempted related formulas, but the calculated results differ significantly from those in Equation 5-3.
Dear @Yingxin.Lv,
You can always convert the stiffness matrix from one coordinate system to another (such as the platform center of mass), e.g., as discussed in the following forum topic: OC3-Hywind RAOs.
Best regards,
Dear @ Jason.Jonkman,
Thank you for your reply, it was very helpful.
Refer to the method in OC3-Hywind RAOs ， I first defined a transformation matrix：
1 0 0 0 89.9155000000000 0
0 1 0 -89.9155000000000 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
K_Lines_cg = TransMat’K_Lines_swl TransMat
K_Lines0_cg = TransMat’*K_Lines0_swl
C_AdditionalDamping_cg=TransMat’C_AdditionalDamping_swl TransMat
K_Hydrostatic_cg :For the C33, the formula : rho * 9.81 * pi * 6.5^2 * 0.25 ,for the coefficients C44 and C55 the formula: rho * 9.81 * (volume_undisplaced * (ZCOG-ZCOB)+pi * D^4/64) (volume_undisplaced=8.0573e+03,ZCOG=89.9155,ZCOB=62)
0 0 0 0 0 0
0 0 0 0 0 0
0 0 333320 0 0 0
0 0 0 2260237325.20468 0 0
0 0 0 0 2260237325.20468 0
0 0 0 0 0 0
Using Strip theory, I computed the added mass matrix with its coordinate origin located at the platform’s center of mass.(Ca=1)
8442486.95734304 0 0 0 231124957.726698 0
0 8442486.95734304 0 -231124957.726698 0 0
0 0 0 0 0 0
0 -231124957.726698 0 16343912822.7079 0 0
231124957.726698 0 0 0 16343912822.7079 0
0 0 0 0 0 0
In the pitch-direction free decay analysis of the structure, apart from the vertical gravity and buoyancy forces that remain constant, the loads acting on the structure are as follows:
F=-K_Lines_cg* q-C_AdditionalDamping_cg* q_dot-K_Hydrostatic_cg*q+K_Lines0_cg;
Using this method, I performed the solution, but there is a significant discrepancy between the results and those obtained from OpenFast. Could you kindly help me identify where I might have gone wrong in this approach?
I hope you can clarify my confusion, point out mistakes in my calculations, or identify any logical or knowledge gaps in my understanding.
Thank you again for your reply and help.
Best regards,
Dear @Yingxin.Lv,
We’ll, I see at least one error in your calculations. Your equation for K_Hydrostatic_cg uses the weight of the full system (rho * 9.81 * volume_undisplaced), but use the CG of just the platform, not the full system. (So, the CG of the turbine is incorrect.) Do you want you reference point to the the platform CG or the full-system CG?
Best regards,
