What was found
ENROUTE, ABOUT 3 HOURS INTO FLIGHT, HAD A SMALL VIBRATION THAT LASTED TWO SECONDS AND WENT AWAY. AT FL360 M.72 KEPT GETTING SMALL VIBRATIONS, ENGINE INDICATIONS WERE STANDARD. AT THIS POINT, THOUGHT IT COULD BE A PRESSURE PROBLEM DUE TO RUMBLE IN THE FLOOR OF AIRCRAFT. DESCENDED TO FL240 SLOWED TO 250 KTS AND RUMBLE STOPPED. SLOWED DOWN, PUSHED UP THE POWER LEVERS, AND THE RUMBLE STARTED AGAIN INTERMITTENTLY. RAISED THE PRESSURE ALT IN CABIN TO LOWER THE DIFFERENTIAL PRESSURE THINKING IT WAS MAYBE A RIP IN THE FUSELAGE BECAUSE OF NO OTHER INDICATIONS. THE RUMBLE RETURNED. DESCENDED TO 15,000FT WERE GIVEN LOWER TO 12,000FT ON POWER BACK THE VIBRATION BECAME STEADY, RETARDED THE ENGINES AND PUSHED UP EACH ONE BY ITS SELF. PUSHED UP NUMBER ONE, THE VIBRATION STARTED TO GET WORSE AND CONSTANT. AT THAT POINT, DECIDED TO DO A PRECAUTIONARY SHUT DOWN OF THE NUMBER ONE ENGINE.