Why does 1991 dodge Caravan vibrate at 30 to 40 mph ONLY when accelerating if it has new tires properly balanced and aligned with good bearings and tie rod ends and engine runs smoothly?

check cv axles. the axle is bad, out of balance. They may not click like you usually have when they are bad.

This happens on acceleration only and will go away when you let off of the gas . replace both, or play one at a time. Chances are they are the factory originals.