I see. Maybe a brake drum catching a brake shoe as it turns? I've had that happen before and it did cause an odd vibration until I had the drums turned. However it was a constant thing unless I was driving at less than 30 mph (didn't notice it then). If your front end is stock and in good nick, I don't see what might cause that sort of vibration except for brakes, wheel bearings, etc.
I had an Oldsmobile which suffered a failing motor mount and when accelerating the fan would rub against the shroud but that was a very obvious thing in terms of the noise it made and I doubt you have that same sort of setup.
I'll keep my thinking cap on here, Dave.