Atif_rasheed might be onto something- if the rubber has warped enough, it might be able to produce a lot of vibration.
That said, my car also vibrates on acceleration- with any amount of throttle input. If it's above 2000 rpm in any gear, it vibrates under acceleration. I knew my right side inner tie rod was done, so i thought it was that. After getting that replaced, getting the wheels aligned and balanced (wanted to be sure), the problem's still there. No idea what it could be now.