Maybe some neoprene for vibrations, it's cheap, or some sound deadening material like dynamat. The dynamat has a better surface and has built in adhesive on the application side. You could wrap the sides and bottom of the box with that and should do the trick.
Lined my entire last car with the stuff, really awesome, kills all vibrations. You will need an application roller.
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It's really great for behind the license plate holder to kill that vibration from big bass. The more you can hit every surface the quieter it will be inside the cabin, but that's extra from what you are asking lol
Another option would be to spray the box with rhino liner, but not sure that would completely work, but it sure looks cool!! Lol
Making me miss my old baby...
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