What was found
AFTER TAKEOFF, ENGINE 3 INDICATED AN ITT OF 1022. POWER WAS REDUCED ON #3 TO NORMAL OP TEMPS. IN THE CLIMB, IF AUTOTHROTTLES WERE USED, #3 ITT WOULD APPROACH TEMP LIMITS WHEN THE AUTO THROTTLES ACHIEVED MCT. AUTO THROTTLES WERE NOT USED AFTER THAT EXCEPT IN CRUISE. IN CRUISE #3 ITT WAS 70-80 DEGREES HIGHER THAN 1 OR 2 AND N2 WAS 3% HIGHER. VIBRATION INDICATORS WERE NORMAL. AFTER REDUCING POWER FOR DECENT, CREW NOTICED A BUZZING NOISE, VIBRATION. THE NOISE CHANGED WHILE MOVING #3 POWER LEVER. SHORTLY AFTER THAT, CAS MESSAGE APPEARED INDICATING A VIBRATION LIMIT. AS PER CHECKLIST ENGINE WAS SHUTDOWN. TEAR DOWN BY STANDARD AREO HOUSTON REVEALED THAT A COMPRESSOR BLADE HAD BROKEN OF THE #2 LP COMPRESSOR WHEEL CAUSING DAMAGE IN THE COMPRESSOR SECTION REULTING IN THE HIGH VIBRATION.