When I lightly touch the top of either the N8 or Mini, I can feel a slight vibration. I am surprised by this because neither device has any moving parts that I know of.
Why does this vibration occur? Is it inherent vibration of the electrical parts within the devices (e.g., resistors, capacitors)?
Listen to what Robert is saying above: electricity is movement. In North America it alternates, or has a frequency of 60Hz, (if you are in Europe it is 50Hz), so it changes direction 120/100 times a second. Changing current causes a magnetic field, so all the metal around this is attracted, then repelled repeatly, very quickly, causing vibrations. Larger transformers- (in your case they are quite small and knock down your 120v or 220v to 9v (etc.) for your power supply) can actually hum- that is the movement of metal in that magnetic field are attracted and repelled so quickly, those vibrations are strong and quick enough to create sound waves in the audible frequency range. I have read that some capacitors, as they change shape during absorbing and releasing energy, can also vibrate.
Would I be well-advised to avoid stacking the N8 and Mini on their power supplies?
Yes, let us know if it sounds better. And if you go so far as some suggestions above regarding footers, the above is the reason companies that specialize in resonance or vibration control state that for components, the best place to put footers is under power supplies.
From Nordost: The performance will be influenced by the precise placement of the Kones. You should seek to position them directly beneath the largest energy source(s) in each item of electronics. These are generally any transport or power supply elements.
Should I simply decrease my coffee intake?
Absolutely not!