Are you sure it is the door? I had a humming / jet engine sound on the passenger side. Turns out my front wheel bearing was going bad. If the pitch changes with the speed, more than likely your bearing.
Does your door lock work on the drivers side? I suppose if it is trying to unlock and lock the door in rapid succession it could be causing a hum or vibration. In that case your door lock would not be working properly.
Finally i found out my cousin had a friend that was visiting from out of town he got him to look at it.he said its not the lock it was the switch for the outside rearview mirror he showed me how to just operate it a few times and stopped the noise and vibration.He said that happens sometime and to just operate it a few times and it unsticks the switch Its ok now and thanks everybody for your help.Oh and my cousins friend works on infiniti's..