A B767-300 EXPERIENCED ENG VIBRATION AND HIGH EGT CRUISING AT FL310. AFTER VIBRATION INCREASED THE CREW SHUT THE ENG DOWN; DECLARED AN EMER; AND LANDED.

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GND OPS WERE NORMAL MINUS DELAYS FOR SVC EQUIP BREAKING DOWN (BELT LOADER); PUSHBACK; TAXI WENT NORMAL. TKOF WAS PLANNED RWY 4L; DE-RATE 1.33 EPR; FLAPS 5 DEGS; TKOF WT 289000 LBS. CLBING THROUGH FL310; VFR; WE FELT A SLIGHT SHUDDER; FOLLOWED BY A HIGH-PITCHED VIBRATION RUNNING FULL LENGTH OF ACFT. IT WAS MORE PRONOUNCED THROUGH THE BODY OF THE ACFT THAN THE FLT CTLS; YOKE AND RUDDER PEDALS. FLT ATTENDANTS CALLED AND RPTED SLIGHT VIBRATION; WHICH SEEMED TO BE COMING FROM OVERWING EXITS. ALL ENG INSTS NORMAL AND WITHIN LIMITS WITH THE L #1 ENG SHOWING A SLIGHTLY ELEVATED EGT; +60 DEGS AND THE VIBRATION GAUGE READING 1.8 - 2.2. THE CAPT USED THE 'CALL ME' FUNCTION AND DISPATCH CAME UP WITH MAINT. WE DISCUSSED WHAT THE POSSIBILITIES COULD BE OF OUR AIRFRAME VIBRATION AND OUR PLAN OF ACTION IN CASE THE CONDITION WAS TO WORSEN. IN THE MEANTIME WE WERE GATHERING WX DATA FOR POSSIBLE DIVERT FIELDS ENRTE TO ZZZ1. THOSE BEING ZZZ2; ZZZ3; ZZZ4; ALONG OUR RTE OF FLT. WE HUNG UP THE CALL WITH DISPATCH AND MAINT AND PROCEEDED TOWARDS ZZZ1. NOT LONG AFTER THAT; WE HAD JUST PAST THE POINT BTWN ZZZ AND ZZZ1 WHEN THE VIBRATION GAUGE STARTED INCREASING FROM 3.2 TO 3.6. WE TURNED OFF THE AUTOTHROTTLES AGAIN AND RETARDED THE THROTTLE TO IDLE TO SEE IF THAT MADE A DIFFERENCE. IDLE SEEMED TO SETTLE THE VIBRATIONS DOWN; BUT THE HIGH FREQ VIBRATION WAS NOT AFFECTED BY THE THROTTLE BEING BROUGHT TO IDLE. STILL; ALL ENG INSTS WERE WELL WITHIN PARAMETERS. WE WERE CONTEMPLATING A PRECAUTIONARY FLAPS 20 DEG APCH AND LNDG; WITH THEN #1 ENG AT IDLE PWR. WE STARTED THE APU AS A BACK-UP IN CASE THE ENG QUIT OR WE WERE GOING TO BE FORCED TO SHUT DOWN THE ENG. WE ALSO PULLED OUT CHKLIST TO REVIEW IN THE CASE A CATASTROPHIC FAILURE OCCURRED. ANOTHER CALL TO DISPATCH AND MAINT. MAINT CAME BACK WITH A POSSIBILITY THAT OUR SPINNER MIGHT BE DELAMINATING. HE NEEDED A VISUAL CHK. THE CAPT SENT ME BACK TO COMPARE THE L AND R ENG. AFTER INSPECTING BOTH ENGS; I FOUND NO DIFFERENCE IN APPEARANCE. I ALSO WENT TO THE BUSINESS CLASS GALLEY AREA TO GET A SENSE OF THE VIBRATION AND IT WAS MUCH MORE PRONOUNCED THAN THE VIBRATION WE WERE FEELING IN THE COCKPIT -- WHICH I RPTED TO THE CAPT ON MY RETURN TO THE COCKPIT. MAINT REMAINED ON FREQ; AS DID DISPATCH DURING THIS CHK. WE WERE GIVEN A DSCNT TO FL290. IT WAS DURING THIS DSCNT THE AIRFRAME VIBRATION INCREASED; AS DID THE ENG VIBRATION GAUGE. IT WAS ALSO AT THAT TIME WE GOT OUR FIRST STATUS MESSAGE; '#1 ENG FIRE LOOP INOP.' WE ALL AGREED THAT A CTLED ENG SHUTDOWN WAS NECESSARY. WE WERE NOW PASSING FL260; WITH A TAILWIND AND 40 NM PAST ZZZ4. I SECURED THE ENG VIA THE CHKLIST. A DRIFT-DOWN WAS NOT NECESSARY AS WE RECEIVED CLRNC TO FL190 AND THE EO ALT WAS FL260 AT A L/D MAX OF 235 KTS. THE CAPT WORKING WITH DISPATCH; CHIEF PLT; MAINT AND MYSELF THE FO PULLED THE WX FOR ZZZ1 AND ALL AGREED THAT ZZZ1 WOULD BE A SUITABLE DIVERT IN POINT AND TIME. WE DECLARED AN EMER AND GAVE ATC ALL THE APPROPRIATE INFO REQUIRED AND RECEIVED PRIORITY HANDLING. THE CAPT CALLED BACK AND ISSUED A CABIN ADVISORY AND SPOKE TO THE PAX. WE LEFT DOWNWIND FOR RWY AND SOME MINOR WX AVOIDANCE. APCH AND LNDG WERE AS BRIEFED WITH FLAPS 20 DEGS; AUTOBRAKES 2 DEGS; GROSS WT 274000 LBS. CRASH EQUIP WAS STANDING BY AND MET US; CHOCKED US; AND THEN CHKED TO ENSURE THAT WE WERE SAFE TO TAXI TO THE GATE -- WHICH WE DID SO; UNEVENTFULLY. IN MY OPINION; THE CAPT PERFORMED FLAWLESSLY -- AT ALL TIMES CALM; ASSERTIVE; IN CTL; MAKING THE RIGHT DECISIONS; AND KEEPING EVERYBODY IN THE LOOP. IT IS A TRUE PLEASURE TO HAVE PEOPLE OF HIS ABILITY AND CALIBER TO WORK WITH WHEN THE CHIPS ARE DOWN.