If I have the desired value of damping for e.g. 2% for the entire model and my model constitutes of two materials namely rubber and steel...I can get the modal frequencies for the entire model and calculate the value of alpha and beta for a range of model frequencies i.e. the Rayleigh's damping coefficients using the equation shown in the image. But how to get the coefficient corresponding to each material? Since FE software like Abaqus asks for the coefficient value of each material.
Rayleigh damping is a global damping approach, i.e.
C = alpha M + beta K
where M is the global mass matrix and K denotes the global stiffness matrix.
I suggest that you use a modal damping approach. Here you can give each eigen mode a different modal damping.
You probably will have to measure these separately for the rubber and the steel. However, damping can also be added by the supports of your material and possible energy leakage to these.
The inner damping of the steel is likely to be very low, while the inner damping of rubber is rather high.
Hate to be a party spoiler but - Rayleigh damping does not have any physical damping phenomenon it mimics, ie it is a purely mathematical concept.
So, you can fit such a model in a bunch of ways. Expect none of them truly to fit what you measure.
If memory serves, ABAQUS can compute modal damping values using the Modal Strain Energy method. In this approach, you assign structural (hysteretic) damping to various material regions and ABAQUS then computes a modal damping C/Critical coefficicent. The approach works as long as damping is light and distributed.
/C
The damping can probably be given as the imaginary part of the E-modules. If the steel is thin and the rubber thick or medium, the shear of the rubber may play a significant role in the damping og the total syste. I do not do much FEA myself, but have tinkered with this some time.
Sanjay R. Kumawat
I have a similar question. How did you solve the issue?
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