I'm not a physicist or engineer however, I do read what those experts have to say about things. One of the major keys to damping vibrations is dissimilar materials. If you GTFS "vibration damping material" and check out the images returned you'll see what I mean.
Your stone rack surface, while rock steady (sorry!), also serves as an almost ideal coupler for vibration. By introducing a dissimilar, flexible, material you should be able to ameliorate the vibration/ringing situation.
Happy listening.