Owners/service Manual problems of the 2015 Chevrolet Tahoe

I purchased my vehicle used on oct 14 2016. I drove it for about 3 weeks in local traffic with speeds 60mph and below with no issues. I then went on a road trip on Nov 7 2016 where I used major interstates that required speeds between 70-75 mph. As soon as I hit the major interstates I noticed something was not right. When the vehicle was set to cruise between 70-75mph and the vehicle reduced from v8 mode to v4 mode the interior of the vehicle began to vigorously shake. The handling and wheel to pavement contact felt stable so I continued my 600 mile trip. At times the shaking conditions made me feel dizzy and somewhat nauseous. I immediately upon arrival at my destination scheduled an appointment at a certified chevy dealer and was seen Nov 14 2016. They test drove the vehicle for about 22 miles and were able to duplicate my problem, however through troubleshooting and inspection could not find anything wrong. I called the number in the warranty manual and started a claim and their resolution was the vehicle was operating as designed,but the gm advisor did say there was a known issue? however they could not tell me why the design made the vehicle do this . To me it sounds like it is a flaw in the design and gm does not know why yet. Through further research I found multiple post and discussions with the same complaint as well as a fox news report where gm spokesman tom wilkinson stated gm knows there is a problem and gm would work with customers case by case to resolve the problem. In my case the resolution was to tell me thats what it was designed to shake. I certainly dont believe what they are telling me . After serving this country in two different combat zones to protect our freedoms its disappointing to know that gm wont stand behind their product as I have stood at the front for this country. L can provide video and dealer service documents upon request.