The case side panels are somewhat like sounding boards. I cut and glued sheet cork ( about 1/8 inch or 3 mm thick) to the inside of the panels to deaden the vibration. You need to be careful not close off vents or get too close to the edges where the panels need to touch the frame of the case. It does make a noticeable difference in noise.
The cork sheets (it was actually a roll) can be bought at an office supply store.