Hyundai Repair: Hyundai Vibration, 2004 hyundai sonata, power steering rack

Question
I own a 2004 Hyundai Sonata (4 cylinder) with 51,000 miles.  For the past 3 - 4 months there has been a very noticeable noise and vibration that has been occurring.  The noise is coming from the passenger side of the compartment and the vibration is at times so intense the rear view mirror and hood visibly shake and rattle.  The dealer has changed the motor belts (not timing belt) and has run diagnostics - no codes were found.  The vibration is felt primarily "through" the steering wheel.  It is felt while in the car is "in gear" and idling; putting the car in neutral will alleviate some of the vibration.  I have had the car looked at on at least 4 occasions and everyone has said this is normal ??  The problem is getting worse, and is not normal.  Those who have looked at it find no diagnostic codes, claim the motor/transmission mounts are fine, appear to be no problems with altenator, water pump, power steering pump (though the power steering rack was changed about 1 year after owning the car), or pulleys/tensioners.  Do you have any recommendations or suggestions ? I have read numerous accounts of people having this same problem and no one seems to be able to have it repaired.  Hyudai Consumer Affairs offered absolutely no help, except to say to take it to another Hyudnai Dealer/Service Department.   Help !!!!!

Answer
Unfortunately, my answer is likely to be little different from what you've already received.  1999-2005 Sonatas with the 4 cylinder engine transmitted significant vibration through the entire car.  The vibration is approximately four times the frequency of a misfire vibration and occurs at idle when the car is in gear.  With the a/c on, the vibration is worse.

The only thing you've said that leads me to believe that this is not normal is that it's worsened over time.  The engine/transmission mounts can settle over time, causing increased transmission of the engine vibration.  In that case, the upper engine mount (rightmost mount) and upper transmission mount (leftmost mount) would need to be replaced.