Removing the vibration from a loud motor
It looks like the motor bracket isn't fastened down properly, which allows it to move. Or maybe it's the point where the motor attaches to the bracket. Turn off the fan, take off the grate, and examine it - maybe you just need to tighten some bolts (if you tighten them, and they work loose again, try putting Lock-Tite on the threads.)

If that doesn't fix it, just leave the piece of wood in place. But if you leave it in there long-term, you'll want to fasten it somehow so it doesn't slide down.