Depending on design, you may be able to place sorbitans spacers (buy sheets or strips) between the granite and whatever is supporting the granite. Then do the same between the supports and the floor (cover the sorbitans sheet that touches the floor with felt to protect the floor if the floor is wood).
I built a "rack" from three 20x40 inch black granite "shelves" and wood supports (hard maple 2x4s glued together for the uprights and 2x4s for the cross supports, the granite is "inserted" into slots in the wood. Everywhere the granite touches is covered by the sorbitan, and the upright supports have sorbitans on their bottom surface covered by the felt. I choose the thickness of the sorbitans to not only support the weight, but for the harmonic frequency that needed to be absorbed.
Incidentally, different granites have different harmonic frequencies. Apparently black granite is the best for audio applications (eg see Acora speakers).
No "ringing", no vibrations, incredible stability.