You can try to find out FRF of the structure and then curve fit using rational polynomial fitting at each modal frequency to get get damping for each mode.

Thank you very much for your response Suman.

I have estimated modal damping ratios, however, my problem is to find damping coefficients in stories.

I was wondering if I could know about this matter.

Hi

If you can calculate the Modal Strain Energy, you can sum this energy per part of your structure and calculate the total structural loss factor a eta_total = sum( eta_j*%SE_j), ehere eta_j is the structural loss factor and %SE is the % of total Strain Energy for area j, respectively. This is called the Modal Strain Energy approach and it works fine up to moderately high damping levels

if you already got modal damping ratios a very simple approach could be to use Rayleigh-damping  for your frequency band.

Dear Claes,

Thanks for your contribution. Actually, I am not familiar with the concept of Modal Strain Energy and I took a look at some of the references but I could not find anything related to this concept.

I was wondering if you could help me regarding finding a reference in this subject.  

Dear Mathias,

Many thanks for your response.

Actually, I am working on modal identification of non-classically damped systems and the Rayleigh-damping model could not be used for my purpose.

Is there any solution to form modal damping matrix from modal damping ratios? (By having access to mass matrix) 

Hi Arash

If you are using Nastran, run SOL 103 and it can directly calculate what you want in terms of %SE for the groups you define. If memory serves, I believe you request ESE output.

If you run Abaqus, no need, I believe the the Modal Strain Energy method already is implemented, at least it was implemented back in the early 90s when I was using Abaqus.

If you have your own code, take a look at eq (11) here: http://web.mscsoftware.com/support/library/conf/wuc95/p03895.pdf

For MSE, here is a short note: https://www.roush.com/Portals/1/Downloads/Articles/Appliance%20Manufacturer.pdf

If you want, you can physically model your dampijg materials and use a Complex eigensolver to compute the loss factors. It is great fun, at least 10 years ago, you got different results in each run starting from the same input data deck. When asking the support, it was explained that computing complex modes and damping is a hobby for gentlemen. If so, welcome and remember - it is damping or the dam-d thing.

In any case, the physics of the matter is that when damping is localized to a portion of your system, say a dashpot at a corner, you should use complex modes. When damping is reasonably well distributed across the system, you can get away with the much simple MSE approach.

Now, computing complex modes is cool. It is fun. But, it is unfortunatly also the end of the road as you cannot use them for modal summation.

You can still do the latter with MSE. If you want to get the best out of both worlds, you need to use MSE + modal substructuring.

Hope this helps or at least confuses you at a new level. :)

Claes

Dear Claes,

It is my pleasure that I have your great comments on this issue.

In fact, I am working using MATLAB and my model is a mass-spring-damper which is non-proportional with respect to mass and stiffness matrices. I could form modal damping matrix in the case of classical damping by simply put them as the diagonal elements of the matrix. On the other hand, this approach doesn't work for non-classically damped systems since the modal damping matrix is not diagonal.

I would definitely examine this approach to form damping matrix.

Thank you very much 

Hi Arash

OK, so your problem is nonlinear then? You can always (hope) to make it piecewise linear and look at damping at various states if this interests you.

Another way then, as it is a sdof system, is to use a simple style approach like the half power bandwidth method (discussed elsewehere on ResearchGate).

You can consider also getting a bit more high tech and use fractional derivatives to describe damping (don't ask me about these, I know only that they exist).

Or, assuming that you have a rigourous mathematical model as your basis and measured data, you can always try a best fit between measured data and your model input variables and work out your parameters from there.

Remember the quote from G.E.P Box - "essentially, all models are wrong - but, some are useful".

(If you do not find the above too depressing, you might find something in my ramblings here http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/ )

Go for useful and have fun in the process of getting there (the most important part)

Claes

Hi.

I'm not quite sure what sort of system you are looking at, as with symmetric positive-definite mass and stiffness matrices in an undamped system, you should be getting purely real mode shapes. And since modal damping does not affect the mode shapes, I don't see how you get complex shapes.

Perhaps you mean that you actually have general damping, which in fact produces complex mode shapes, and you want to find a modal damping approximation. Perhaps you can then do what is suggested by Argyris and Mlejnek in the book "Dynamics of Structures".

Your problem is Mu''+Cu'+Ku=f. Let KX=LMX be the eigendecomposition of K and M. Now, if X^t C X = diagonal, then you would have modal damping. As in your case it is not, Argyris and Mlejnek (if I recall correctly) then suggest that you can approximate C in your system with D=MX diag(X^t C X) X^t M. That is, you change your basis to the undamped modal basis, and then ignore the coupling that remains between the modes.

Hi,

I am not sure if I understood your problem correctly. Nevertheless, I once read this paper

http://dx.doi.org/10.1016/j.jsv.2009.02.005

regarding the decoupling (like modal decoupling) of systems (mass-spring-type) which are not classically damped. Maybe this hepls.

Cheers, Sebastian

you can look at the paper: A Note on Non-proportional Damping. You should be able to download it from this ResearchGate site.

best,

firdaus udwadia