BeamDyn: add point masses and show eigenfrequencies

Hello,

I have browsed the forum for quite a while but couldn’t find a method how to add point masses to the BeamDyn rotor blades (to account for e.g. measurement devices or bolts). Is there any possibility to do so? If not, what would be a suitable procedure to include something similar to point masses to the rotor blades?

Also I am wondering if it is possible to determine the Blade eigen frequencies from the BeamDyn model. Considering the latest “Future Work” from the BeamDyn User guide (“Implementing eigenvalue analysis”) I don’t expect this to be possible, but I still wanted to ask.

Thank you for your help and happy new year,
Paul Feja

Dear Paul,

BeamDyn does not currently have the option of positioning point masses along the beam. Of course, you could always specify a short section of the beam to have a different mass distribution (i.e. spread the point mass over a finite section of the beam added to the distributed mass), which would then be included in the model when invoking the well-resolved trapezoidal quadrature (Quadrature = 2).

We are currently working together with Envision Energy to introduce linearization capability into FAST models with BeamDyn. Once that effort is complete, you will be able post-process linearized models (including states associated with BeamDyn) and perform eigenanalysis (e.g. using MBC3) as is done now for models without BeamDyn. Until then, you can derive the natural frequencies of any FAST model by post-processing the results of time-domain simulations where the model has broadband (e.g. white noise) excitation, as has been discussed elsewhere on this forum.

Best regards,

Dear Jason,

thank you for your help. I will try to implement the point masses as you suggested and look for the topic regarding white noise excitation of the turbine in order to determine the eigen frequencies.

Best regards
Paul

Dear Jason,
currently I am facing the same problems than Paul: I am performing FAST simulations with BeamDyn and I would like to get the rotorblade eigenfrequencies. I simulated a power production time series with turbulent wind and performed an FFT on the blade root loads. The peeks of the FFT show the eigenfrequencies quite well, but it would be nice to have a “pure mathematical” result of an eigenvalue analysis, too…

You mentioned your work with Envision Energy on the linearization of FAST models with BeamDyn. Are there any news concerning this topic?

Thanks a lot and best regards,
Jochen

Dear Jochen,

The ability to linearize an OpenFAST model with BeamDyn enabled (for direct eigenanalysis, etc.) was included in the release of OpenFAST v2.0 (and so is also included in the current OpenFAST master branch, v2.3, where additionally some BeamDyn-related bugs have been fixed).

Moreover, we’ve worked further with Envision to introduce additional linearization capability, including improved ways of calculating steady-state solutions (including trimming of controller inputs) and visualization of full-system mode shapes after the eigenanalysis. These features have recently been merged into the dev branch of OpenFAST.

Best regards,

Dear Jason,

thank you for the quick response and for the good news about the linearization with BeamDyn!

Indeed, I was able to run a linearization with my FAST/BeamDyn model. Unfortunately, I don’t have Matlab (so I could use MBC3 for the calculation of eigenfrequencies). So I tried to calculate the eigenfrequencies of the turbine model on my own:

  • Read the A matrix from the *.lin file
  • Calculate the (complex) eigenvalues of this matrix
  • Calculate the square root of the eigenvalues
  • The real part times 1/2pi equals the eigenfrequency.

Unfortunately, this results in a lot of eigenfrequncies that do not really fit to the peaks of my FFT analysis of a DLC1.1 time series. I get the same result, if I analyse the A matrix of a *.BD1.lin file, which contains only the state matrix of the blade.

Do you have any hint, what I am doing wrong? Or do you have a hint to another already existing tool for the calculation of eigenfrequncies?

Thank you and best regards,
Jochen

Dear Jochen,

NREL does not support another post-processor for the linearized matrices separate from the MATLAB-based MBC3 tool. You can likely get by using the free Octave tool instead of MATLAB.

I’m not following why you’d take the square root of the eigenvalues and look at the real part. For a simple linear mass-spring-damper (m-k-c) system, the complex eigenvalue pair (lambda) would be:

lambda_1,2 = -omega_nzeta +/- omega_nSQRT(1-zeta^2)*j

where,
omega_n = SQRT(k/m) = natural frequency in rad/s
zeta = c/(2momega_n) = damping ratio in fraction of critical
j = SQRT(-1) = imaginary number

So, the natural frequency (omega_n), damped frequency (omega_d), and damping ratio (zeta), can be calculated from the eigenvalues by:

omega_n = SQRT( Re(lambda_1)*Re(lambda_2) - Im(lambda_1)Im(lambda_2) )
omega_d = Im(lambda_1)
zeta = -( Re(lambda_1) + Re(lambda_2) ) / ( 2
omega_n )

(which works for any value of zeta and generalizes to second-order systems with many degrees of freedom for complex pairs of eigenvalues).

Best regards,

Dear Jason,

thank you again for the quick response and the description of the correct way to calculate the eigenfrequencies of the turbine.
It seems, that I understood something wrong from the several references I found in the net. Using your formula result in eigenfrequncies that fit quite well to the results of the FFT analysis. :slight_smile:

Thank you, you guys are doing a great job!
If you are ever in Hamburg, please let me know. We should go for a beer or two… 8)

Best regards,
Jochen