Why does the gas pedal of a new 2008 Hyundai Azera continuously vibrates after 20 miles per hour?
I would guess a wheel out of balance, likely the left front.
In any case, why are you asking us? It should be under warranty and you should be complaining to the dealer and have them fix it. You don’t need to tell them what is causing the vibration, you just report it. They won’t pay any attention to what you think it is anyway.
I agree with Mr. Meehan.
The solution to your problem is spelled w-a-r-r-a-n-t-y.
Take it back to the dealership, and allow their mechanics to figure out the problem.