At this point you have identified the source of the noise, but not necessarily the cause. Much like putting a blade of grass between your thumbs to make a reed whistle, the vibration associated with variable speed equipment is caused by airflow over that reed; in this case, the louvre. Variable speed blowers operate at a whole range of different speeds, it could be that one of those speeds just so happens to cause the airflow across the louvre to vibrate in symphony (like the blade of grass). However, it is more likely that the vibration is caused by excessive air velocity. It could be as simple as adjusting the airflow at the equipment; making short work of the problem. More likely, the return air system is too restrictive. Restrictive duct will cause increased face velocity at the grilles. More air pressure and movement are more likely to set the louvres vibrating.
Finding the cause of duct restrictions, and eliminating them, will net two benefits. It will help avoid weird noises, and it will allow the blower motor to run at a lower torque. The biggest reason for motor module failures is restrictive ductwork. The little thermistor in the module overheats when the motor has to work too hard. You can get rid of a future breakdown while you are getting rid of the weird noise.