Mercury Grand Marque 2002 V8 - 160,000 miles

My car seems to vibrate at different speeds. Its not tires because its a quick vibration or shaking.At first I thought it was just the road. I had the rear axels replaced and shortly after that I started noticing a vibration that felt like the road was a washboard. I did not think nothing of it then it started happening more. It feels just like you run over a washboard road for a split second sometimes longer. I would turn around and go back over the same spot to see if it was the road and I could not make it do it. My coils are going bad but that is a miss not a vibration. Any know problem with these cars that cause this.