What was found
CLIMBING FL350 HEARD A LOUD BANG/POP SOUND FOLLOWED BY VIBRATION. INDICATION OF ENGINE PROBLEM, FLASHING RED OUT OF LIMITS ITT ON RT ENGINE. PULLED BACK RT ENGINE THROTTLE TO IDLE. ALL OTHER ENGINE PARAMETERS NORMAL. A MILD BURNT OIL SMELL OBSERVED IN CABIN. VIBRATION CONTINUED, SHUTDOWN RT ENGINE, OBSERVED APPROX 14.5 % N1, 2.5% N2, VIBRATION DECREASED. DECLARED EMERGENCY, MADE UNEVENTFUL LANDING. INSPECTED, NO EVIDENCE OF CAUSE. INLET, FAN, EXHAUST, & VISIBLE TURBINE WHEEL SHOWED NO SIGNS OF DAMAGE. IMPENDING BYPASS DIFFERENTIAL PRESSURE SWITCH NOT POPPED, OIL QTY NORMAL. NO EXCESSIVE OIL FOUND IN COWLINGS. MX BORESCOPED, METAL SHAVINGS/FLAKES LAYING IN BOTTOM OF TURBINE CASE SECTION OF ENGINE.