2006 Saturn Ion • 4 cylinder FWD Automatic • 101,000 miles

I have a 2006 Saturn ion which vibrates upon acceleration. I travel on a four lane road and it does not start vibrating until after about 15 minutes. When I let off the gas it is smooth. Have had front end aligned, new tires, etc. Have read about harmonic balancer, motor mounts, etc. How do I diagnose the problem from here?
March 29, 2011.

Is it a bad vibration upon excell like the front end is shaking really bad?If so I would suspect a axle issue.

Oct 17, 2012.