There really isn’t enough data to work with here. What are the requirements? Do you simply not want to hear any noise from them coming from the cabinet? Or are there large amps sitting right next to sensitive and calibrated testing equipment requiring complete de-coupling from any vibrations caused by the nearby amps?
Obviously making the noise go away requires much less than completely seperating any physical connection causing the propogation of sound and/or kinetic vibrations. To isolate the sound you can use rubber feet under the amps and add material to all sides of the cabinet to absorb energy. Keep in mind you will still need ventilation so equipment doesn’t cook. But you’ll have to use vents leading into some other space where you aren’t as concerned about the sound. You should also have weather stripping or similar to close air-gaps around doors and spaces in shelves not used for ventilation.
You’ll have to experiment and test against what you are expecting.
Happy tunning.