How Can Vibration Damping Materials Reduce Machine Noise?

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I am trying to reduce the noise created from a machine that makes contact (impact) with a thin plate. I just don't have anyone to bounce ideas off of.

I can change the support geometry to whatever I want as long as it will with stand a static load and the impact. I can handle this, but the support structure would be my boundary conditions for the thin plate.

I would like to put a layer of dampening material under the thin plate to convert some of the energy to heat. I don't know if this is even possible of worth my efforts.

Does anyone know of any natural metals that have a dampening property, but are durable as well?

It would be neat if I could setup the geometry to push the vibration of the plate to outside of the audible frequency threshold of the human ear, if that would be possible.

The model I want to use is the wave equation with an impulse input, but I don't really know how to model a multilayered material
Any Ideas would be greatly appreciated.
 
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Does anyone know of any natural metals that have a dampening property, but are durable as well?
Rubber?
What counts as "durable" etc depends on what is doing the colliding ... a rubber bumper won't do much for a jack-hammer but is fine for a door.
It would be neat if I could setup the geometry to push the vibration of the plate to outside of the audible frequency threshold of the human ear, if that would be possible.
The effect of damping is not so much to change the frequency of the vibration as to reduce the amount of vibration.
You could use the damper to reduce resonant vibrations - like putting your finger on a bell - but you'll still hear it.

You could set up the system so it has a different natural frequency when struck - and put a damping bumper between the machine and the plate.