One problem related to steering wheel vibrate has been reported for the 2005 Jeep Grand Cherokee. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Jeep Grand Cherokee based on all problems reported for the 2005 Grand Cherokee.
As I was leaving a shopping center about 40 miles away from my house my Jeep and as I entered onto the interstate the Jeep acted like I was having a flat tire with the steering wheel shaking and giving me a lot of vibration and the flop flop sound you get from a flat tire. I stopped and got out but no flat tire, loose lug nuts or anything I could find. Put flashers on and headed up the road slowly not going over 45 mph. It finally quit and I was able to increase speed. It continues to have this wobble sound along with the steering wheel shaking off and on. I did some research and the only thing matched what happen was the Jeep death wobble. Some vehicles have had a recall on this but I don't see any for my year.