Purchased a 2014 chevy 4wd crew cab, 3.43 rears, 20" goodyear wranglers about 3 months ago. I had the shake too. I fortunately had the shake resolved by my dealer after 2 failed attempts. I had to call GM and threaten lemon law, but they came through and the truck is smooth now. The replaced tires first time around and roadforced them. It didnt work. 2nd attempt - another new set of tires and roadforced again. No good again. Finally they ordered a new driveshaft and Michilin LTX, roadforced and finally smooth as glass. All I can say is have patience and if your current dealer isnt cooperating then contact GM and have a case opened and tell them your troubles with your dealer. I truely believe that the dealers are baffled by this and are trying anything to fix. GM engineers are responsible for this. They shouldnt have released a truck with issues like this. Patience... its hard but its out of our control.