I would start by removing the grills from the fan assembly. See if that helps. Air moving makes very little (if any) noise. Its what the moving air hits that reverberates the sounds we hear. If the motor is mounted on the grill then I would cut away as much of the grill as I could. I would also look at adding things to dampen any vibration that the fan is making and transferring...rubber washers,etc. Good luck.