I have a 2004 Pontiac Grand Prix GT. There is a mild vibration in the front end when the suspension is compressed and I'm accelerating. If I let off the accelerator, it all goes away. I've rotated the tires and it's still there.
When you accelerate a vehicle there is a weight transfer from the front to the rear. This means the front suspension will lose its loading and extend its springs. You need to have your front end inspected, paying particular attention to the drive shaft and hub bearings.