Just solved a vibration problem on our 2007 AWD that had been getting increasingly worse since about 24k miles. It would seemingly only happen when you
applied pedal, in that regardless of the speed, if you took your foot off accelerator, vibration/shuddering would stop. Increased as you went up in speed. Seemingly tires, wheel balance etc. were ruled out since the vibration was not just from steering wheel and would stop taking foot off accelerator. I thought maybe torque converter/tranny, cv joint or ?!
Service manager drove it and said he had never seen that problem before but the folks at Kachina Cadillac went after it and finally said it was the drive shaft. I was skeptical as it had not been touched since new, is located where it could not have been struck by anything and there were no marks on it. They agreed we could not have damaged it in any way, they replaced it under warranty and described it as "out of round" and you could see it was not straight when you rotated it on the car.
Well, it cured the issue completely so if any of you have a similar issue, have them check the driveshaft....I know it sounds nuts but it fixed the problem.
Vibration from 35mph upward 
