What is the AWD dial between the front seats set at?
Would 4WD been on, on dry pavement? You could be feeling driveline judder, which would be normal.
If in Auto, in other words 2WD, could be CV joint issues. Its just out of basic warranty so tread carefully
I know in my GC there is no 2WD. Auto in mine still has all 4 wheels engaged and there is no 2WD setting. Depends on the transfer case employed, the Pentastar equipped GC's are the same, as is the Durango. Not sure what the case is on the Cherokee, but it may be similar (just throwing that out there).
OP: Sounds like it could be feathering on the outside or inside edges of the tires, is there any visible?