WDB ACR DIVERTED TO JFK FROM LGA AFTER ENG SHUTDOWN DURING DSCNT.

Narrative

AT INTERMEDIATE LEVEL OFF AT 26000 FT ON DSCNT INTO LGA; WHEN PWR WAS ADVANCED #2 ENG BEGAN TO VIBRATE AND ENG VIBRATION MONITOR #2 SHOWED A MARKED INCREASE. FURTHER DSCNT WAS MADE AND AT LGA 225/PLUS OR MINUS 30 DME (11000 FT MSL) WHEN PWR WAS ADVANCED #2 VIBRATION MONITOR PEGGED AT JUST UNDER 4.0 ON BOTH PICKUPS ALONG WITH ASSOCIATED LIGHTS ON PLT'S CAUTION PANEL COMING ON. THE ENG WAS SHUT DOWN PER 'ENG FAILURE' CHKLIST AND FLT HANDBOOK EXPANDED PROCS WERE COMPLIED WITH. DURING THE ABOVE WE (I) WERE STILL RECEIVING AND COMPLYING WITH ATC/APCH INSTRUCTIONS AND HAD DSNDED TO 7000 FT MSL AND 4000 FT MSL FOR A VISUAL APCH TO RWY 22 AT LGA. LGA APCH WAS ADVISED OF THE SHUTDOWN AND TOLD THAT WE WERE TALKING WITH COMPANY AS TO WHERE THEY (MAINT) WANTED THE ACFT -- LGA OR JFK. WE WERE ADVISED IT WOULD BE BEST TO GO TO JFK. ONCE WE ADVISED LGA APCH THAT WE WISHED TO DIVERT TO JFK THINGS BECAME VERY 'BUSY' AND I (CAPT) NEGLECTED TO OBTAIN A RELEASE FROM THE DISPATCHER. HUMAN PERFORMANCE: DEGRADED DUE TO TIME ELEMENTS FROM ENG FAILURE/SHUTDOWN; DSCNT AND APCH CLRNCS; FREQ (RADIO) CHANGES. THIS DEGRADATION ONLY APPLIES TO MY FAILURE TO OBTAIN A RERELEASE TO JFK; ALL NORMAL AND EMER PROCS WERE COMPLIED WITH IN AN EXCEPTIONAL MANNER.