Is your Ford Explorer 4wd or all wheel drive? Making sharp turns on dry pavement with the 4 wheel drive engaged will cause the drive line to bind up which could be described as a vibration. 4 wheel drive systems are not designed to operate in 4 wheel drive mode on dry pavement. They do not have a center differential which will allow for the different wheel speeds between the front and rear wheels. All wheel drive systems are designed with a center differential which will compensate for the different wheel speeds. If your Explorer is 2 wheel drive this should not be a problem. IF your Explorer is 4 wheel drive your transfer case may be in the 4 wheel drive mode. If your Explorer is All wheel drive you may have in internal problem with your transfer case.