[lrubin28]

I'm not sure which category this question belongs in, or if it's even a chemistry question - I think it's part physics, part chemistry!? 

I'm making electronic drums. On the top of the drum there's a flat surface (the drum head) you hit with a stick anywhere on the head.  The diameter is say 14 inches.   A couple of inches below the head, is the bottom of the drum - a piece of flat metal that's attached to the inner wall of the drum with brackets.  Adhered to the center of the metal bottom, is a flat, round piezo which is wired to the electronics that make the drum sound.  The piezo is about 1 inch in diameter.  Sandwiched between the bottom of the drum (with the piezo) and the drum head, is "some type of foam". 
The idea is that you hit the drum head and the energy is transferred to the head, through the foam, and then hopefully to the piezo in the center of the bottom, which if triggered sends a signal to play a sound.  I'm trying to figure out what type of foam would be best for this, so that no matter where you hit the drum head it's able to trigger the piezo.  I've spent a small fortune on various foams so far and I'm getting closer, but there's got to be a more scientific approach!
Why not just mount the piezo to the drum head?  Because hitting it with the sticks would break it quickly.  Why foam?  Because you want to be able to play using headphones and not have others hear you - so you can't use anything hard in the middle, and you still want a little bounce.  So what type of foam would be best for transferring the energy from the large head, to the small piezo? Low density? High Density?  I don't understand how the kinetic energy (?) moves from one thing to another.  If something is good at absorbing shock does that mean that it converts energy to some other form that dissipates the energy which wouldn't be good for triggering the piezo, or does it mean that its good at passing the energy from one end to the other (from the top to the bottom) which would be good for triggering the piezo? I guess this question is part physics (energy), part chemistry (foams), part electronics etc.  And sorry for being so long winded....

[Enthalpy]

Hi Irubin28, welcome here!

You experimented, and that's the right thing to do. Music instruments are very complicated, poorly understood, and our perception of sound even worse so. Even where physics does bring a little bit to instrument design, it's often qualitative understanding only.

You have a "piezo" sensor. Is it a microphone, sensitive to air pressure, or a vibration sensor that picks movements? If it's a microphone, then it gets its signal from the air inside the drum, rather than through the foam's movements. A foam is then useful to insulate the microphone from outside noise, like shocks, especially a shock from the stick transmitted through the head and the bottom to the microphone. The shock would make a very different sound, short and metallic and lean, very different from what we perceive from an acoustic drum - not desired (hence the sensor is probably a microphone). So the first function of the foam would be a microphone suspension, for which it should be soft essentially.

Foam has an other role in loudspeakers: it dampens the air oscillations - I can't tell if this is desired in your particular drum. The effect is often understood to produce losses through the air's movement, but this isn't the main action in a loudspeaker. As air gets compressed and expanded in a vibration cycle, it heats and cools. This temperature swing is tiny but very significant for the behaviour of a gas. Some heat is transferred to the solid from the air when the pressure is bigger within a cycle, but this is slow, so that the solid doesn't give this heat back to the air on time when the air loses pressure, and the air having lost heat has also a lower pressure when it expands back: it has lost energy.

In a smooth quarterwave cylinder, rubbing losses would be twice as strong as thermal losses, but in loudspeakers, the foam is against the walls, where the air speed is small, so it acts by the heat far more than by the movement. The open cell foam brings much contact area with the air in order to increase the losses. And because the air, not the solid, limits the heat exchange, the foam's material isn't very important for the losses: only its area counts, plus practical considerations.

A possible different role would be to dampen the vibrations of the bottom. Maximum damping - if desired! - would then prefer the lossy material to be denser (plain synthetic rubber) and in strong contact with the bottom, possibly glued. This requirement differs from air damping; maybe one material fits both, maybe two materials are better. I'd rather try instead to have the walls and bottom of plastic shells (something like ellipses) instead of metal sheet like a cylinder and a flat bottom. It depends on the instrument: a snare drum prefers vibrations everywhere, a bass drum prefers damping.

So for your drum, you may perhaps try to suspend the sensor (if it's a microphone) by rubber rings to hear if you want to dampen the oscillation additionally, and if yes, select a convenient (healthy, durable...) soft open-cell foam, and adjust its volume and the size of its cells.