If the problem genuinely is resonance, then the offending part of the case has a natural vibration frequency which is the same, or similar to, one or more of the internal motors.
Vibration frequency depends on the mass/inertia of the panel concerned, so adding some mass to it will change its natural vibration frequency. This can be done by adding a few pieces of thin sheet lead. Attach them to the centre of the panels with those double-sided sticky pads.
If your problem is simply excessive noise from within the case, then sound insulation is the way to go.
Cheers,
JaX
