Resonance of cabinets or a chassis makes me shake my head. SO Many times, I have used a vinyl damping sheet to take care of the problem. I just put it on say the top cover of the component. I can use the word drastic here and not be exaggerating, since I will tap a component cover and it will literally ring like a bell before placing a sheet in place. After the sheet is placed, I get a small dull thud.
In your case, I wonder if this isn't just treating the symptom, since I have never felt a chassis vibrate as drastically as you describe. If in fact if it is a reaction to a magnetic field from the amp, I would think that taking the cover off would expose a large magnetic field to your system components that are in proximity of that field.