Just thinking about ideas..
Vibration is caused by mis-balance thus we can (a) reduce the initial vibration, (b) lessen the contact points or (c) convert the energy of the vibration to another form of energy (such as heat)
Noise can also be due to resonance - standing waves that reinforce or cause other non-connected bits to vibrate in sympathy.
Couple of thoughts:
a) balance the rotor shaft of the pump - just like garages do for your wheels when you have new tires. Downside is that this involves taking it to pieces..
b) reduce the contact points - audiophiles (like us but instead of taste they go nuts over hearing) use points (like pin points) to separate loudspeakers from the floor to reduce vibration.
This works for vibration which isn't going to cause physical movement as there's little to prevent sideways movement.
c) use of specialist damping rubber converts the vibration to heat. Engine mounts are a good example - the key is to get the right material. When the material is designed for heavier things (such as engine mounts) the material will be too stiff and the vibration will just be transferred. Materials for too lighter purpose mean that device would move too much with vibration possibly hitting the endstops (knocking).
For DIY this is trial and error.. for the scientific we're looking at the vibrations - taking FFT analysis and selecting the right materials to dampen the most powerful frequencies.
You could use steel beams to flex in sympathy but 180degrees out of phase.. thus cancelling out the more powerful frequencies too. This could be done with active electronics too.. although the less electronics close to water,steam and my coffee the better..
d) It could be possible to suspend the noisy bits too.. with dampening springs or oil cylinders too..
e) not having square 90 degree flat inside panels will help prevent the creation of standing waves in the internal space. Additionally FFT analysis would help identify the lengths between panels to avoid.
Adding acoustic dampening (such as suggested car engine bay damping material) will help too.
f) lastly - proper structural bracing will prevent panels vibrating in sympathy to vibration frequencies. Just how loudspeakers are braced to prevent the walls from creating unwanted frequencies.
It's also important to ensure there's no openings that would act as a 'port' for waveforms set up - just like the ports on loudspeakers.
*pats his Yew Harlech Castle speakers, Musical Fidelity A220 and Myryad MC100 CD player..
Barista - applied pre-emptive hydro-thermodynamicist.