A G-IV FLT CREW AT TOP OF DESCENT EXPERIENCED EXCESSIVE TGT IN #1 ENG. THEY SHUT DOWN THE ENG; DECLARED AN EMERGENCY; AND LANDED SAFELY AT THEIR DESTINATION.

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AT THE TOP OF DSCNT; CREW WAS CLRED TO CROSS 35 NM N OF ZZZ1 AT FL240. CREW WAS UNABLE TO MAKE SUCH A STEEP DSCNT; AND WAS RECLRED TO CROSS 25 NM N OF ZZZ2 AT FL240. DURING BEGINNING PHASE OF THE DSCNT; UNUSUAL VIBRATION OCCURRED. CREW INITIALLY BELIEVED THIS TO BE FROM THE SPD BRAKES; AS THERE WAS NO VIBRATION INDICATION ON THE ENG VIBRATION METERS. CAS MESSAGE OF ENG EXCEEDANCE OCCURRED; ACCOMPANIED BY HIGH TGT ON THE #1 ENG. CREW INITIATED AND COMPLETED APPROPRIATE CHKLISTS PER COMPANY SOP. THIS LED TO SHUTDOWN OF THE #1 ENG. CREW DECLARED AN EMER WITH ATC AND WAS IMMEDIATELY CLRED DIRECT TO ZZZ. CREW CONSIDERED POSSIBILITY OF DIVERTING TO ZZZ3. CREW ELECTED TO LAND AT ZZZ DUE TO THE FOLLOWING FACTORS: 1) ZZZ3'S PRIMARY RWY HAD A XWIND; BUT THE WIND AT ZZZ WAS A HEADWIND. 2) CREW HAD ALREADY SET UP AND BRIEFED THE APCH INTO ZZZ. 3) CREW WAS ALREADY ESTABLISHED ON AN EXTENDED FINAL TO THE FAVORABLE RWY AT ZZZ. 4) CREW IS FAMILIAR WITH ZZZ AND FELT THAT SETTING UP FOR AN APCH INTO ANOTHER ARPT WHEN SO CLOSE TO THE RWY THEY WERE PREPARED TO LAND ON WOULD HAVE DISTR THEM FROM HANDLING THE EMER. CREW LANDED UNEVENTFULLY AT ZZZ.