What could be causing the thumping noise while driving?

What is your question?

Recently I've noticed a thumping noise, similar to a helicopter sound when I am driving. It speeds up when I do and slows when I do, no sound with sitting still. I do not hear any difference with turning either direction. My car has also recently started to vibrate/shake with driving. I had a waffled tire on the front driver side and put new tires on the back and the 2012 Goodyears on the front, but the sound is still there. I was severly rear-ended a couple of years ago with $11,700+ damage done to my 2008 nissan altima coupe and the repairs were done. They did not total the car. Can you help me figure out what I might ask the Goodyear guys to look at when taking my car for check? Thanks.