I need a vibration dampening rubber-like material

I need to 3d print a structure that is made out of a flexible rubber-like material that is good at dampening vibrations with a medium level of softness. I'm using it as a clamp so I don't want it to squish that much when compressed but I don't want it to be rock hard either. I want there to be some give but not to the point where it squishes flat.
There seems to be a reasonable selection of rubber-like materials, which one should I choose?

polyflex from polymaker works well.
Prints without much hassle and is firmer than ninjaflex.

You could just do a few layers top and bottom with ninjaflex.