Input forces in linearized system

Wind & Water Structural Analysis
1

Hi,

I would like to experiment a bit on the dynamics of the linearized model of a wind turbine. For that purpose i would like to be able to input a force (as a time series in any of the degrees of freedom but the most important ones to me are blade tips in and out of plane and tower top FA and SS).

For now let us assume that the turbine is at a standstill to not complicate things further although the ultimate goal is an MBC transformed system.

The problem that I am facing is the incompatible nature of openfast’s linearized system. the outputs y are just what I need - positions velocities accelerations and forces - but the inputs do not ,include forces or accelerations, velocities, displacements.

My understanding is that the states vector x consists not of physical but rather modal degrees of freedom and their time derivatives. These modal coordinates are presumably coefficients of the predefined polynomial mode shapes of elastodyn’s input, so this is not a classical modal transformation using the modal matrix Phi whose Columns consist of the eigenmode vectors of the system:

image

I have 2 Ideas as to how I could achieve my goal.
One would involve recovering the M, C and K matrices from the A matrix assuming

image
image305Ă—151 3.11 KB
then M^-1 *K = - A21 and M^-1**C = A22.

Assuming that the modes are mass normalized and M = I then i can recover C and K.

But then I would need the Phi matrix which I am not sure how I would obtain.

The second Idea is to somehow modify openfast to include as inputs forces acting on modal degrees of freedom.

Option 3 which I am almost certain is not possible is modifying OpenFast to give me directly the M, C and K matrices but as far as I know openfast doesn’t even calculate these internally.

Which would be the best approach for my problem? Have i missed something more elegant and obvious?

Best regards,

Vasilis

2

Dear @Vasilis.Xenodochidis,

Within the linearization functionality of OpenFAST, while the standard set of inputs does not contain loads applied to the blades and towers, the full set of inputs does. That is, the ElastoDyn module receives loads as input from other modules at the blades, hub, nacelle, tail fin, tower, and platform. These inputs, as well as all other module-level inputs, will be included in the linearized state-space matrices when LinInputs = 2 is set. Beware though, that, this setting will generate a lot of inputs, so, the matrices will be quite large. To understand what you are looking at, as with any linearization analysis, I would start with a simple model with limited DOFs and functionality enabled and build complexity in steps.

Best regards,

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