Woo Hoo.....finally somebody somebody else with a buzz/rattle. Search some of my posts. Mine "started" with only happening at 3800ish RPM between shifts revs coming down (I have a 5 speed manual) but now appears frequently at about 3000 rpm very noticeable on the highway at light throttle. Doesn't do when it accelerating only under no/light load. Dealer has already changed flex pipe 2-3 times, cats, exhaust manifold, motor mounts. Only thing that made it go away was flexpipe change and that only last a couple hundred miles. Purchasing dealer won't do anymore, factory rep was no help. Submitted all customer complaints etc and got nowhere.
Car is going to my independent shop in a couple weeks for inspection anyway. I'm going to try some clamp on weights other companies use (BMW, Ford, Chevy) to change harmonics of exhaust system (NVH). It basically adds mass loading to the metal (like Dynamat for doors etc for stereo stuff). My shop looked at also while on lift and easy to duplicate and if somebody holds by flexpipe area it goes away. No other companies at the time made aftermarket flexpipe but I haven't looked recently. I might ask my shop about "replacing" it with a universal one if there is room to move the clamps where it bolts on even if they need to be cut and rewelded further back.
Just got a "new" Hyundai dealer close by so might give them a try to see what they say.
I'll check back when I try it.
Like mentioned try to determine exactly under what conditions it happens like described above light/no load, turns etc.