Quote from David on 25. July 2023, 14:18

Hi Tim,

QBlade uses stiffness matrix (K) proportional Rayleigh damping, the damping matrix (C) is then calculated as:

C = beta * K,

where beta is the stiffness proportional Rayleigh damping coefficient.

The conversion between beta and the fraction of critical damping Zeta of a certain modeshape is:

beta = Zeta / (𝜋 *  f) ,

where Zeta is the fraction of critical damping (between 0 and 1) and f is the frequency of the mode in Hz.

You can also checkout the following link on this subject: https://wiki.csiamerica.com/display/kb/Damping+coefficients

Typically the damping coefficient is set for the 1st natural frequency of the system. In the latest release of QBlade it is also possible to assign distributed damping beta coefficients via the structural tables, but this is only required for special cases where a structure might be equipped with additional damping elements at specific parts of the structure.

BR,

David

Quote from TimHH on 27. July 2023, 12:05

Thank you, David! This helps a lot and will try to catch up on this topic soon.

Quote from TimHH on 14. August 2023, 19:52

Hello David,

My first damping setup should be fine now and it was quite easy according to your instructions. Nevertheless, could you please provide some more support on the following questions?

1) Stiffness proportional Rayleigh damping means that the mass proportional term is neglected – right? Could you please help me why is this should be a valid assumption?

2) Guidelines like DIBt 2012/2015 (Richtlinie für Windenergieanlagen) recommend a constant log. decrement for structural tower damping if no further details are available. To my understanding this is not possible with QBlade’s damping approach. Do you have any guidance here?

Thanks again and best regards
Tim

Quote from David on 17. August 2023, 20:34

Hi Tim,

let me try to answer your questions:

1) You are correct, when using only the stiffness proportional term the mass term is assumed to be zero. Using both the mass and stiffness term offers more control over a wider frequency range of damping responses – however using only the stiffness proportional term greatly simplifies the damping definition and is a valid assumption when damping effects are small. Also, Rayleigh damping itself is only a modeling approach that comes with certain limitations, such as the assumption of linear damping behavior and constant damping coefficients across all frequencies.

2) One of the limitations of the Rayleigh damping approach is that it allows tuning towards a constant logarithmic decrement only within a specific frequency range. Despite this limitation, Rayleigh damping remains widely used in many engineering practices. One could interpret the guidelines in a way that the statement referns to the logarithmic decrement of the side-side and front-back tower modes. Its very well possible to tune the logarithmic decrement to yield a certain value of critical damping, see the attached image where we tuned to a critical damping of value 4.5% and compared with OpenFAST.

BR,

David