What was found
WE WERE CLEARED TO CLIMB TO 15000FT ON RUNWAY HEADING. CLIMBING THROUGH 7000FT A VIBRATION WAS FELT, FOLLOWED BY AN ENGINE VIBRATION CAS MSG AND ENGINE EXCEEDANCE CAS MSG. THE LEFT THRUST LEVER WAS PULLED TO IDLE (THE ENGINE EXCEEDANCE CAS MSG WENT AWAY) AND AN EMERGENCY WAS DECLARED. A VECTOR TO DOWNWIND 36R WAS GIVEN ALONG WITH A DESCENT TO 5000FT. I SET THE AVIONICS FOR LANDING AND RAN THE ENGINE VIBRATION CHECKLIST FROM QRH 2 WITH INSTRUCTED TO LEAVE THE ENGINE RUNNING AT IDLE. THEN THE SINGLE ENGINE LANDING CHECKLIST WAS COMPLETED. THE ENGINE WAS SHUT DOWN VIA FADEC INSIDE OF THE FINAL APPROACH FIX DUE TO A RISE OF ITT AND VIBRATION (THE ENGINE EXCEEDANCE CAS MSG REAPPEARED). DUE TO THE CLOSE PROXIMATE TO LANDING, WE ELECTED TO SELECT THE ENGINE RUN SWITCH TO OFF TO AVOID INADVERTENT RESTART VIA FADEC. THRUST REVERSER WAS NOT USED ON LANDING. THE FMS INDICATED A 700LB OVER WEIGHT LANDING. MAINTENANCE PERSONAL OBSERVED METAL DEBRIS INSIDE THE MIXING NOZZLE AFTER THE EVENT.