Q&A

 Master

It hard to guess at the source of the problem with out being able to drive the car first hand and get an impression of what is actually going on. It is hard to discern if the problem could be caused by the engine ,transmission or chassis/suspension.
The vibration is intermittent and from your description it sounds like you think the problem is related to taking a right turn. It could be a bad half shaft. I had a car recently that beat us up. We drove the car 20 miles couldn't duplicate the customers complaint. He came in drove the car and the car vibrated like crazy we drove the car with him an additional 30 miles and never felt the vibration. I drove the car home that night and I thought the car was going to shake its self apart at freeway speed. On the way into work the following morning the car was perfect. Eventually after replacing a bad engine mount which did not fix the problem we put a half shaft in the car and it fine ever since. Try rotating the tires first, and see if the problem changes. Hyundai as a car manufacturer allow owners and independent garages access to Service manuals, service bulletins ect..... for free!
Check out : http://www.hmaservice.com/
perhaps you may find your answer here. Would love to know what you find.

have you replaced your timing belt. There are actually two on that car a small one that usualy slips and starts to go first. It will cause the entire dash to vibarate but car will still run and still have power. They are supposed to be replaced every 60k I have over 180k on mine and all three times just over the 62k mark my car did what you are saying and the small timing belt had slipped.