5 Replies Latest reply on Nov 2, 2018 3:19 AM by Erik Kostson

# Rayleight damping alpha, beta value suggestion request.

Hello,

I'm try to run nonlinear dynamic simulation to bellow show structure.

The result looks abnormal. I believe the reason was wrong input of alpha, beta.

I used alpha-0.11 beta -0.000289

please suggest propper alpha, beta value to use with this.

3D drawing attached here with.

Force-1 = force -2

Thank you.

Udaya.

• ###### Re: Rayleight damping alpha, beta value suggestion request.

If you have the modal damping for the modes of interest, and their frequency than there is a relation between that, and the alpha and beta coefficient.

Below is an extract from Strand7 Help, were the alpha and beta are given explicitly:

Further more if you assume that the two modes of interest have the same modal damping (different freq. of course), then these relations/equations become trivial and are as shown below:

This is all explained in the solidworks help (just search for Rayleigh damping).

Finally typical damping ratios values (Greek letter  z in the above equations, is modal damping ratio) for steel welded frames can be between 0.5% - 2% (0.005-0.02).

• ###### Re: Rayleight damping alpha, beta value suggestion request.

Hi Erik,

Thank you for your valuable suggestions.

I'm not familiar with structural design tasks.

So at once i'm could not understand how to decide two chosen frequencies need  substitute to equations?

I already have verified damping ratio by studying the output graph of linear dynamic simulation done with same model.

My  self It is difficult to understand what expane in the SolidWorks help.

Udaya.

• ###### Re: Rayleight damping alpha, beta value suggestion request.

Say for example the frequency range of interest is ~ 4 - 40 Hz with a damping of about 1.5 % at these two frequencies, then alpha and beta are as shown below (you can calculate that yourself with the above equations, convert first from Hz to rad/s, that is omega=2*PI*Frequency):

We can see above that effective damping ratio in this range will typically be about 1 %, which is reasonable for welded steel frames and a bit on the conservative which is good.

I should mention also that the best way like you say to get modal damping is to measure it physically using say experimental modal analysis. These measured values can then be used in the FE model (the values of 0.5% - 2% I stated are typical taken from literature, so not exact for every case). Also very important for you to have in mind because I think you confusing things, is that damping is measured from physical tests as mentioned, not from FEA. To FEA we input the measured damping, thus it will be whatever we put in, so FEA is not a magic box where we can get the damping.

• ###### Re: Rayleight damping alpha, beta value suggestion request.

Thank you very much Erik.