It is usually the fan being out of balance on these units that generates the vibration. Because the fan blades are usually made of plastic the fan blades cannot be easily reshaped to attempt to quiet the vibrations. The Panasonic ones use a quieter technology for the blades (many computer whisper fans are Panasonic).
Based upon the diagram, it looks like the damper is enclosed in plastic housing that clips to the exterior surface of the metal frame. If the o.p. has access from the attic, it will be be easy to pop it off and check it. If no attic access, then it might be possible to see from the interior of the box, but I can't tell from the diagrams. -- nohup rm -fr /&