Tar panels, ranging from 2mm and up are used in the automotive industry to keep flat sheet panels from vibrating by adding inertia/mass. Otherwise the car would literally be a bell. You can also find variations in the automotive sound system world where people apply massive amount of such panels to keep the car from resonating. Most often, those panels have a peel-off/stick-on back. Therefore they are very easy to use.
Dynamat is the original supplier. But they are very expensive. You can find similar products for much cheaper.
http://www.b-quiet.com/extreme.html
For one tenth the price, you can go to your local Lowes renovation center and get roofing material. ;-)
http://www.scroungers.net/t475-cheap...ive-to-dynamat
You can find thicker stuff from other sources. The thicker, the better. I also suspect that every single panel in your A7 would benefit from a sheet or two of such sound deadening material to keep them from vibrating. Old wood, thin wood, dry wood will easily resonate.