Vibration that apears just sometimes going up a hill loaded?

by Ken
(Charlotte, NC)

I have vibration in my 2000 Peterbilt 379 with N14 engine. When its empty can not feel any vibration, ones it gets loaded even with a light load going up a hill will run strong, but if you take off your foot from the accelerator pedal / going up hill / then you press it back the whole truck will start shaking / on 13th gear / if you keep pushing the pedal it will shake more, if you release the pedal and push it again will run with no problem. Doing it sometimes more sometimes less, bob tail wont do it at all.

I left the truck at Peterbilt dealer in Charlotte NC, everything checks out perfect, they said its in great condition but when I get it loaded still shaking. Changed the turbo boost sensor, turbo compressor, u joints on the drive shaft, all fuel filters even the one in the fuel pump, center bearing didn't get resolved?