Damping between shelves and sandbox

use something like delft clay or petrobond casting sand. 

Maybe try plywood instead of mdf or solid wood. Works very well for me ... no tt experience though. Best plywood would be "Panzerholz" (I think it's called phenolic plywood in English). Very heavy, used for cars and trucks and tanks (Panzer in German), but very expensive too.

If you must use sand let the dry sand do the isolating but everywhere else you wan to use extremely hard materials so that energy is rapidly Evacuated out of the system.That’s why I eschew soft materials like Sorbothane and rubber and lead and relatively soft cones like carbon fiber and brass. Step up to the plate and get some hardened steel cones or the NASA grade ceramic cones from Golden Sound. Springs are a better solution from a SQ perspective, that’s why the sandbox guy at Bright Star went to springs a long time ago. Twenty some odd years ago to be precise. Hel-loo!

Springs just as goefkait said.
Preferably under a mass loaded shelf.

And put your loudspeakers on springs with a solid substrate underneath, it will improve EVERYTHING! Obviously finding the correct springs for the load they are bearing is important.

"IF", you mix any liquid medium with the sand. OR, it is simply very humid and the sand becomes damp. Either will totally negate the ability of the sand to act as a "transducer". Where the vibration causing the resonance problem changes from a "kinetic" energy to a "thermal" energy. The heat then simply dissipates into the ambient air. "This is accomplished by the friction, "Sand grain against the other vibrating sand grains" = heat. Induced by your gear.
 Constrained layer damping with  "Coupling/decoupling" between layers   works great and you may "Tune" it as needed.
 There is a reason that "Tone woods" are called "tone woods"! 
It is because of how they each handle different vibrations, or "Resonance" as they do. MDF is crap. It is dead, sawdust and glue.
The best has always been certain Mahoganies and Rosewoods but they are mostly illegal now to buy or just unavailable.
 Sugar or Rock Maple, Black Walnut and Cocobolo seem to cover the spectrum the best now for what's available. "Some" Mahogany from Costa Rica", "Santo's Mahogany". It is "Ok to good", but hard to find and you have to know the wood to pick it out. 
Dupont's, "Corian" works well though. But you have to play with the thickness. It is harder to get right than say, "Maple"..
 The gear stands I make start with a "Slab" I buy. Usually 2'to 4' wide. 16' o 20' long and at least 3-1/2" inches thick. "5" thick is best but very rare.
 Out of a slab I get 5-6 "Plinths". Once planed and squared and sized I add layers of Corian and then other woods as needed for the purpose. With springs, bearings, "sorbothane", and also assorted "Whatchamacallits", that have developed.
 Complete they are 3" - 8" thick. The ones I make with a "Void" for sand, shot or oil? Those are first sealed "Inside and outside", with two part "System Three", epoxy with an access that is sized to use an "Expanding rubber boot" to keep it sealed.
 No leaks and no dust.
 But "Damn" they are expensive. A raw "slab" of the hand-picked hardwoods, "Tone woods",  avg. about $2000 at my cost.
 But hey, "I figure that I'm worth it"! And they are fun to make!