This article is from the Chrysler-Plymouth-Dodge FAQ, by Dr. David Zatz with numerous contributions by others.
Paul Schikora suggested this might be the low gas alert being sounded due
to the gas sloshing around in the tank.
Pete Morrissette said he also had a dinging sound, but not the same kind:
his Voyager's sliding door pinged/dinged on bumps and turns. Paul Schikora
said the bolt connecting the door to the arm (which slides in the track at
the front top of the door) sometimes loosened. To check, grab the door
there and try to push/pull it; if it moves in and out, the bolt must be