One problem related to steering wheel vibrate has been reported for the 2011 Ford Explorer. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2011 Ford Explorer based on all problems reported for the 2011 Explorer.
I was traveling approx 60mph when an alert from the dash sounded, the steering wheel vibrated and 2 messages appeared on the onboard messaging system: 1) "power steering assist fault" and 2) "service advance trac". At that time I lost all power steering ability. I am very fortunate that I was driving on a straight stretch of road at the time as I am unsure if I could have kept the vehicle from going off of the road. I pulled over at a gas station and turned the car off. I restarted the car approx 5 min later and it had no warnings and the power steering had been restored. The next day, the exact same thing happened, except I was going approx 10mph turning left into the Ford dealership to let them look at this problem. They informed me today that they needed to order a new "rack" and that the part was "backordered" and had a delivery date of November (today's date is 8/27/12).