I have a closed box fan motor above an insulated false ceiling. I asked the builders to put acoustic absorbing material around the motor to absorb its sound but am not happy with the deep resonant sound which still existed.

Today I investigated and found that the cause of this sound is the vibration of the bottom wall of the fan box which as you can see in the photo is where the fan rests. I can actually stop the noise by pushing the wall with my hand from underneath and causing it to flex inward.
Can anyone suggest a way to deaden this vibration and subsequently this noise?