I have a 345 as well and have chased most of the vibrations out. Many other have done the same on this forum. A few additional questions if you don't mind:
Vibrations and shimmys are different things (IMHO) can you describe a little more about it? Low or high pitched? Does it change when under power, coasting or decelerating? Where along the floorplan is the approx location of the vibration? Does the coach actually move up and down or side to side?
There are a number of things to check. Tires, suspension, shocks, brakes,driveline, axle, etc. Give us some more to go on and we might be able to get you close to the root cause. In the meantime try a few searches on "driveline vibrations" or similar searches on this forum for some good background information.
1986 Airstream 345 Classic Motorhome