We have a Carrier heat pump system in our home, and the blower is located in the attic. When it is especially cold, the blower runs on high (there are three levels: high, medium, low). During this time, the blower vibrates the upstairs walls and doors so that we hear constant rattling noises. Is it possible for a technician to adjust the blower so it can't run so hard? Or is it possible that the ducts are not big enough to handle the air flow? (This is a system that replaced the original one a couple years ago) We can temporarily resolve this problem by removing the air filter at the return air vent, but that is not ideal. We do not have this issue during cooling.
Have you tried placing a clean fresh filter? Probably, but I have to ask. The real problem is the blower isn't well balanced and other issues exacerbate it. I've not heard of anyone balancing blowers, but I don't know everything.
Another possible issue is the blower anchorage is loose. Some are mounted through resilient mounts. The rubber may have perished, fresh mounts could help solve the problem.
An under sized duct system could be a contributing factor, addressing that would be quite expensive. Be sure all your registers are fully open. There may also be balancing dampers in the ducts, you shouldn't mess with those unless they look almost fully shut. Or it could be the blower is over sized and you do not need that much volume.
Sometimes the speed can be adjusted. If it's truly over sized, you may get by with only medium speed. Depending on your system, an inappropriately low fan speed can be dangerous. Be sure a qualified technician is making the decision to lower the speed.
Could be a 2 speed fan. If it vibrates, "...when it's really cold" then it could vibrate when the thermostat calls for more heating and requires the higher fan speed.