If you think your going to bug your animal with vibration, put it on Aspen.
You are going to get way more 'dampening' from a 1 inch layer of shredded Aspen than from any rubber mat, etc.
...but... Are you sure there is even a problem? Is anything else wrong with shed, feeding, big changes in temperament, etc)
If not, everything is probably just fine.
(Often some of ours pass-out with face mashed up against the front of their tub. I can turn the big lights on and clean others for 2 hours..... Most of them don't wake up until I actually touch them.)