## Forum

# Rayleigh Damping

Quote from TimHH on 25. July 2023, 09:18Hello David,

I’m currently busy with the

conversion of blade/tower damping from Bladed to QBlade. While Bladed is using the damping factor (or: relative damping) per mode shape, QBlade is using a single Rayleigh damping parameter per blade/tower. Could you please let me know your recommendation for the Rayleigh damping setup?Furthermore, I also noticed that the blade/tower structural data tables now allow the

optional definition of distributed damping coefficients (Rayleigh beta coefficient). Is this distribution following the structural stations or is it defined per mode shape? Do you also have a setup recommendation here?Best regards

Tim

Hello David,

I’m currently busy with the **conversion of blade/tower damping from Bladed to QBlade**. While Bladed is using the damping factor (or: relative damping) per mode shape, QBlade is using a single Rayleigh damping parameter per blade/tower. Could you please let me know your recommendation for the Rayleigh damping setup?

Furthermore, I also noticed that the blade/tower structural data tables now allow the **optional definition of distributed damping coefficients (Rayleigh beta coefficient)**. Is this distribution following the structural stations or is it defined per mode shape? Do you also have a setup recommendation here?

Best regards

Tim

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

QBlade uses stiffness matrix (

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

C = beta * K,where

betais the stiffness proportional Rayleigh damping coefficient.The conversion between

betaand the fraction of critical dampingZetaof a certain modeshape is:

beta = Zeta / (𝜋* f),where

Zetais the fraction of critical damping (between 0 and 1) andfis the frequency of the mode inHz.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

betacoefficients 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

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 14. August 2023, 19:52Hello 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 termis 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. decrementfor 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

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, 20:34Hi 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

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

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