B757 flight crew experienced high N3 vibration at FL300 during descent. At 11000 feet the crew elected to shut the engine down and declare an emergency. Single engine landing ensued at destination.

Narrative

Normal flight until the beginning of our descent on the arrival. At approximately 30;000 FT we noticed an amber N3 vibration indication of 4.3 to 4.6 on the number 2 (right engine). I called for the QRH; accomplished appropriate checklist and was able to clear the fault. During descent adjusted #2 power to see at what power setting the engine could be used without exceeding limits. During our descent we received several N1 amber warnings also. But the indication eventually settle back to indicating a N3 of 5.0. Close to 11;000 FT with the engines at idle we declared an emergency with approach control and informed them of the nature of our problem; number of people on board and remaining fuel. We then notified the flight attendants TEST and had them prepare the cabin for landing. We then accomplished the engine failure/shutdown checklist. Then the one engine approach and go around checklist. We contacted Tower and were given a discrete frequency. We asked Tower to activate airport rescue and fire fighting to assist us after landing. We also asked the Tower to contact appropriate agencies. We then were cleared for a visual approach. We flew a slightly extended downwind; intercepted final at approximately 9 miles and accomplished a one-engine landing in accordance with the one engine approach procedure. We cleared the Runway and stopped the aircraft. At our request; airport rescue and fire fighting personnel inspected the right engine and reported no obvious damage or leaking fluids. We taxied to the gate with airport rescue and fire fighting escort; shut down and deplaned using normal procedures. The incident was documented in the Maintenance Log and was thoroughly debriefed with maintenance personnel who met us at the gate. A Flight Attendant Supervisor also met us at the gate to check on the cabin crew and their ability to continue their sequence. Of note; no representative from the Flight Department met us either at the gate or in the terminal for the next 90 minutes while we sorted out by telephone and balance of our sequence and other issues. Total elapsed time from declaring the emergency until parking at the gate with approximately 15 minutes. Given our recurrent training; all procedures; events and participation by all player's flowed essentially as well as we could expect. Many thanks to my crew and my co-pilot for an excellent job done.