This sounds like a driveshaft problem like the center support or flex joint is out allowing the driveshaft to move around causing the vibration.
Here are diagrams to help you see what I am talking about.
Check out the diagrams (below).
Please let us know what you find. We are interested to see what it is.
Images (Click to enlarge)
Sunday, April 29th, 2018 AT 12:14 PM