Two points:
1) Mr. Grammar says: Dampening is misting with water. Damping is absorbing vibrational energy" :^)
sorry, that one's a pet peeve; I'm pretty sure the battle is lost, but like those mythical Japanese soldiers lost in South Pacific island jungles, I keep fighting.
2) Mechanical vibration exists in capacitors, due to the electrical attraction as the voltage between electrodes varies. This is in addition to the electrical resonances that earwaxxer describes. It is quite audible with some caps! There are many modes of mechanical vibration, some of which have little or no motion at the outer surface, and others than can be damped at the outer surface.
3) There are in practice quite a large number of damping materials and methods that have nearly no effect at all, and very few that are truly effective. This is true of almost all vibration problems I've run across, and I've run across quite a few! That's why sharing experiences on a forum like this is so valuable - we are not all Thomas Edisons, willing to try 10,000 different materials before finding baked sewing thread makes a decent light bulb filament!