I've never had that particular vibration problem. What material are the doors made of & how are they attached to cabinet? Can you remove just the doors?
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If I had to guess without seeing the cabinet, I'd suspect it most likely that the airborne vibrations are exciting the cabinet door. That in turn is probably causing the door to vibrate against the cabinet frame and generating audible vibration. Inspect the cabinet and see if this looks possible. If so, you can try to damp the interface of the door and cabinet to ameliorate the issue. To start diagnosing a solution, I'd try using small bandaids or blu-tack dots applied to the inner edge of the door frame where it meets the cabinet. If this helps, you can cut black felt into thin ribbons and apply them to the door frame for a more attractive solution. Maybe just a few felt dots sold in home repair stores would be enough. If the cabinet door is making the noise, something like a body panel dampening sheet sold for auto sound applications should work (they ain't pretty though.). You can buy cheap stethoscopes at some auto parts stores to help diagnose and isolate vibrations also.
Thanks for the responses. Beavis, the doors are maple and due to WAF definitely not an option to remove them from the cabinet.
Photon46, I initially detected the problem you describe of the vibration at the interface of door and cabinet and have managed to dramatically reduce this using a felt lining in the frame which makes it a tight fit. Whilst the noise is reduced significantly, I can still hear some resonance noise in the door panel itself. I think I might try your idea of dampening sheets which I can secure to the insides of the doors (so ugliness not an issue). Thanks for the suggestion.