after turning off the car a few minutes later a loud vibrating noise comes from on 2003 Jeep Grand Cherokee

where the ac/heating control panel in the middle what is that noise

Try turning off all heat/ac controls a minute before turning engine off to see if noise still there. Sounds like actuator noise in the mode selector. If system works ok, drive on!
1 more answer
It could be the AC compressor. Inspect the compressor and see if any oil is starting to leak from the shaft seal area. The internal AC compressor swash plate bearings could of failed allowing excessive axial play and compressor shaft leakage. Go ahead and inspect your shaft seal-I would venture to say it's leaking now or will be leaking shortly if you continue to use the AC.