Multiple transformers in one chassis interacting and humming

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I've 5 transformers of various sizes in one 19inch 2U steel chassis. When powered up individually each is quiet. As more are powered up though they start to hum and progressively get noisier. I presume they are interfering with one another via the chassis. Other than separate chassis are there any remedies?
 
1. Try to use dielectrics between transformer and chassic. Sometimes it can help, but poorely.
2 . Better way to use shields on each transformer.
3. Try to use shield from permalloy or something like that. It can be found in old TV.
 
5 in one box? Forget the buzz, what you are making? lol

As a resonance issue, we could look at mechanical damping. Either physical isolation from the chassis, or stiffening the chassis. Recently I was moving a weight around on a panel to find the sweet spot to stop 3 fans rattling it. Lots of weight in the wrong place was useless, but a little in the right place fixed it. The issue is one of resonance, which I stopped from building.
 
Ah, you think it's an accumulation of resonances? I hadn't thought of that! 😱

The sound does appear to come from the transformers as opposed to the chassis, although they could be resonating more of course.
 
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