The attenuation data (boundary admittance) can be measured using an impedance tube experimental setup. 

Are you looking for the bulk material properties or the boundary properties?

Also my one concern would be that since the material is most likely fabricated by layering heated material on cooler material, the resulting material might not be acoustically isotropic. in other words, the material may have properties that are non uniform through the bulk. However, this would only be the case for small wavelengths in the material (relative to the thickness of the layers), and you are describing a low frequency application.

Also in response to the first answer, in an elastomeric material, there can be a bulk attenuation term due to internal damping. this is a result of complex sound speed (resistive term).

One way to measure this would be to use the material as a damping layer, between a vibrational source and a large static mass (i.e. test bench). have accelerometers on both sides of the material, and measure the transfer function.

start with one dimensional motion in the direction of the vibration propagation, and measure over a set of low frequencies to get a transfer functinon. You can then try modeling the system as a mass on a spring with damping and fit the parameters.

This might be all you need.

One way to measure this would be to use the material as a damping layer, between a vibrational source and a large static mass (i.e. test bench). have accelerometers on both sides of the material, and measure the transfer function.

You can read in this link 

Regards

Lubis, Muhammad Zainuddin, M.Sc

http://onlinewww.jpier.org/PIER/pier139/01.13030507.pdf

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