# Eigenvalue in BModes

Dear developers:

I am confused by the eigenvalue of BModes. Below is my BModes results for 5MW wind turbine blade:

The frequency seems to be reasonable. However, the eigenvalue is very high. If my understanding is correct:

``````frenquency = sqrt (eigenvalue) / 2 / pi
``````

I am confused why eigenvalue is so high here.

Regards,
Ran

Dear @Ran.Tu,

Good question, but I’m not sure I know the answer. I’ve really only paid attention to the frequencies and mode shapes included in the BModes *.out file.

Best regards,

Thank you Jason. Indeed we only need bending mode shapes in BModes to be inputted in Elastodyn.

I have one more question. Could you please share a link talking about how to conduct eigen-analysis of entire system in OpenFAST. I also searched in the forum…trying to study

Regards,
Ran

Dear @Ran.Tu,

The linearization and eigenanalysis process has been discussed several times on this forum, e.g. here: Campbell Diagram & MBC3 output relation.

See also the linearization, Campbell diagram, and mode shape visualization documentation found here: GitHub - OpenFAST/matlab-toolbox: Collection of Matlab tools developed for use with OpenFAST.

Best regards,

Dear Jason,

Thanks for your shared link. I have conducted the eigenanalysis with only one operating point (wind speed =0, rotor speed = 0) using runCampbell.m. I noticed that I got four files:

``````Campbell_ModesID.csv
Campbell_OP.csv
Campbell_Point01.csv
Campbell_Summary.txt
``````

But I am confused by the comment : “The mode identification currently needs manual tuning (modes might be swapped)” in runCampbell.m. In Campbell_ModesID.csv, it listed mode number table:

I guess the sequence is identified by Matlab code based on Campbell_Point01.csv.

1. But I am confused how we judge if the sequence needs to be tuned?
For example, in Campbell_Point01.csv mode 2 is:

Here I see “State has max at mode 2”. Only “ED 1st flapwise bending-mode DOF of blade collective m” and “ED 1st tower fore-aft bending mode DOF m” is 1 which possibly means these two states has max. So they are possibly dominant in mode 2. Then I compared “Mode 2 signed magnitude”. From other post, I found it means the contribution of each state to this mode. As the maginitude of “flapwise bending mode of blade collective” is larger, so I guess flapwise bending mode of blade collective is the most dominant in mode 2.
But in Campbell_ModesID.csv, mode 2 corresponds to 1st Tower FA. I do not know whether my judgement is correct (mode 2 is 1st Blade Flap (Collective)).

2. For mode 5:

No state has max at mode 5. How can I judge which state is the most dominant? Directly based on the magnitude? As magnitude of flap-wise bending of blade collective is largest. Does it mean flap-wise bending of blade collective is the most dominant in mode 5?

3. For each state, is it only able to correspond to one mode? For example:

In mode 14, “ED 1st edgewise bending-mode DOF of blade collective m” has the largest magnitude. It seems that this state is dominant. But if I have confirmed this state correspond to former mode (i.e. mode 7). Thus, this state can not represent mode 14 any more. I have to turn to find the second largest magnitude (i.e. drivetrain rotational DOF).

4. When judge the most dominant state, is “has max” more important than “magnitude” ?
For example in mode 13, I found 2nd Tower SS has max, but its magnitude is not the largest.

But in Campbell_ModesID.csv, I found mode 13 corresponds to 2nd Tower SS, while model 14 corresponds to nacelle yaw, although you can see the magnitude of nacelle yaw is larger than the magnitude of 2nd Tower SS.
So I guess " has max" is more important than “magnitude” when judging the most dominant state.

Regards,
Ran

Dear @Ran.Tu,

Yes, this is where it takes practice to properly identify the modes. It is difficult to identify a mode in isolation of the other modes. And each full-system mode can have contributions from all DOFs. The “state has max at mode” and “mode signed magnitude and phase” are guides that should help you interpret each mode, especially in relation to other modes.

Regarding (1), blades are much more flexible than towers and it is common for the fore-aft deflection of the tower to have a lot of blade flapwise deflection as well. Mode 2 looks like 1st Tower FA to me.

Regarding (2), mode 5 looks like the 1st Blade Flap (Collective) to me.

Regarding (3), the highest modes are the most difficult to interpret. I would first determine the lower modes and the highest modes can be identified by which modes are left.

Regarding (4), I agree that “the state has max at mode” is likely a stronger indicator than “mode signed magnitude”, because it is important to identify modes in relation to the other modes and because each mode has contributions from all DOFs.

Best regards,

Thank you Jason,

1. I do not know two words in Campbell_ModesID.csv: Progressive and Regressive. Is progressive regarding blade cosine? Is Regressive regarding blade sine?

2. Campbell_Point01.csv contains Natural (undamped) frequency (Hz), Damped frequency (Hz) and Damping ratio (-).
Could you please correct my understanding?
2.1 Natural frequency only relies on structural properties and constraints (like mass and stiffness).
But for damped frequency, damped frequency will account for damping ratio we defined for blade and tower (assuming I only use elastodyn or subdyn). So if I change the damping ratio, damped frequency will change accordingly, but natural damping will not change.
2.2 Could you please share a link or explain what damping ratio in Campbell_Point01.csv mean?

Regards,
Ran

Dear @Ran.Tu,

Regarding (1), progressive is used to represent a mode whose natural frequency in the fixed frame of reference is higher than the collective mode and regressive is used to represent a mode whose natural frequency in the fixed frame of reference is lower than the collective mode.

Regarding (2), I agree with your interpretation. Damping can be associated with structural damping, structural dynamics terms (Coriolis, gyroscopic), aerodynamics, etc.

Best regards,

Dear Jason,

1. In Elastodyn, we defined a critical damping ratio for blade and tower. But when implementing this critical damping ratio in code, it is transformed to a stiffness-proportional constant.

2. After doing linearization and running runCampbell.m Matlab code, we also get a damping ratio:

In above figure, Damping ratio is a stiffness-proportional constant for entire system’s stiffness matrix.

3. Here damping ratio (stiffness-proportional constant) = 0.003683, natural frequency = 0.313523, so the critical damping ratio:

``````critical damping ratio = stiffness-proportional constant * pi * natural frequency
=  0.003683 * 3.14159 * 0.313523
= 0.00362
= 0.36 %
``````

I am not sure whether this derived critical damping ratio is reasonable. This is an onshore wind turbine, without wind and wave. I assigned 1% critical damping ratio for both blade and tower in Elastodyn. No intial rotor speed was assigned. I would assume that hub mass and nacelle mass increase the mass matrix for entire system, and then decrease the critical damping ratio to 0.36% for entire system.
Regards,
Ran

Dear @Ran.Tu,

1. Correct.
2. No; the damping ratio computed by the linearization process is not a stiffness-proportional damping constant. Rather, the damping ratio computed by the linearization process is the damping ratio, which is the fraction of critical damping.
3. For a single DOF system, I agree that the `damping ratio = stiffness-proportional constant * pi * natural frequency`, but the linearization process computes the damping ratio and not the stiffness-proportional constant.

Best regards,