Hi all.
In this post, @Jason.Jonkman mentioned to use only the static components (axial load and bending moments) and not the dynamic component to calculate the fatigue at a certin section, i.e., for example for local axial load, MαNβ FKxe and not MαNβ FMxe.
That post is quite old now, so I was wondering if, for the subdyn in OpenFAST 3.5.4, this is still the case, or the sum of the two signals should be used since the code has been improved?
Many thanks
Dear @Maurizio.Collu,
This statement still applies to SubDyn, despite recent improvements. The statement arises from physical arguments, not from limitations to SubDyn. The basic explanation is as follows:
If you have a linear mass-spring-damper (m,c,k) system with displacement (q) and applied force (F), the equations of motion are m * qdd + c * qd + k * q = F, where d is the first-time derivative and dd the second-time derivative of q. The reaction force (Fr) in the foundation is Fr = c * qd + k * q, which by the equations of motion is equivalent to Fr = F - m * qdd. When damping is small, the reaction force reduces to Fr = k * q, whereas m * qdd is not a good representation of the reaction force. This is why we recommend using the static component (k * q) rather than the dynamic component (m * qdd) as a proxy for reaction loads in SubDyn. The damping component (c * qd) is not readily calculated by SubDyn, but is typically small compared to the static component.
Best regards,
Many thanks, @Jason.Jonkman , for the quick answer and explanation.
I can follow your reasoning, and it makes sense, but I am probably missing something basic, and apologies if this is a dumb question, but why the reaction force (Fr) is Fr = c * qd + k * q and not Fr = m * qdd + c * qd + k * q? Is this because we are talking about the foundation, i.e. the seabed, that is not characterised by a mass?
If that’s the case, I suppose it is different if we talk about the reaction force in a generic joint in the structure, not part of the point in contact with the seabed, but between two beam elements each one characterised by a mass/moments of inertia?
Basically, the question stemmed from the fact that I would like to calculate the fatigue in a section between two beams of the structure, that is not in contact with the seabed: should I take into account only “K” forces, or “K+M” as intuitively I would do?
Dear @Maurizio.Collu,
Summing the dynamic and static components is a reasonable approximation of the applied force for small damping (m * qdd + k * q = F for a single mass-spring-damper with small damping), but is not a reasonable approximation of the reaction force (Fr).
Considering one element out of a bigger frame structure can be thought of as a mass-spring-damper system in series. For a system with two masses, two springs, and two dampers in series, the force transmitted from the spring-damper connecting the outboard mass to the inboard mass (Fr12) is Fr12 = c * (q1d-q2d) + k * (q1-q2) = F1 - m * q1dd, where 1 and 2 represent the force/motion of the 1st and 2nd mass. Again, for small damping, this reduces to Fr12 = k * (q1-q2).
For the equivalent in SubDyn, this difference in displacement is accounted for in the static component (based on a generalized stiffness matrix and displacement vector, k * q), so, the end result is the same as from my single mass-spring-damper example.
Best regards,
Of course! Many thanks @Jason.Jonkman for the clear explanation.