You can obtain the damping matrix directly as an output of your model. You have to specify a separate step (" *STEP " is the option in the input file), after which you have to specify the following:

*MATRIX GENERATE,DAMPING

*MATRIX OUTPUT,DAMPING

and when you run the model, a file with extension .mtx will be created. This file contains the elements (values) of the damping matrix of the model.

Hi,

 May be following link will help you.You can evaluate damping ratio if you know alpha ,beta and eigen value.

http://www.oulu.fi/tietohallinto/unix/abaqus_docs/v6.13/books/gsk/default.htm?startat=ch07s02.html

Hi, 

 One can find the damping ratio from experimental analysis. But I can help you by providing material about "How to get M, K, C from experimental modal analysis (EMA)" . Somehow this material gives you overall idea about M C K matrices.

Hi,

If you impose to the material its alpha and beta coefficients it means that you are considering a proportional damping of the material (Rayleigh damping). This means that:

[C] = alpha[M]+beta[K]

if you can know the eigenvectors matrix of your system [phi], you can apply the modal transformation to your system, that is for the damping matrix:

[phi]'[C][phi] = [Cmod]

and for mass and stiffness matrix:

[phi]'[M][phi] = [Mmod]

[phi]'[K][phi] = [Kmod]

where [Cmod] [Mmod] [Kmod] are all diagonal.

Now you can basically compute your damping factor matrix [zeta] where each element on the diagonal is:

zeta_i = c_i/2(sqrt(k_i*m_i)

If the eigenvectors normalization is done properly, you will obtain a damping factor matrix [zeta] with the diagonal elements ordered from the first related to the first mode, and the last related to the highest mode.