AN A320 EXPERIENCED ENG VIBRATIONS DUE TO INLET COWL ICE ACCUMULATION AND DIVERTED TO AN ALTERNATE ARPT.

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ON A FRIGID AND BLUSTERY MORNING IN ZZZ1 ON JAN/SUN/05; THE WX WAS WORSE THAN INCLEMENT. IT HAD SNOWED FROM 6-12 INCHES THE PREVIOUS DAY AND THERE WAS STILL LIGHT SNOW. THE TEMP HOVERED AT -7 DEGS C. IT WAS NOTICED DURING THE WALKAROUND THAT THERE WAS SNOW AND ICE OVER MOST OF THE ACFT. THERE WAS NO DOUBT THAT WE WOULD HAVE TO DEICE THE ACFT. DUE TO THE CHAOS PRIMARILY ATTRIBUTABLE TO THE WX; OUR XA45 DEP DID NOT LEAVE THE GATE UNTIL XD12. THE TAXI TIME TO AND FROM THE DEICING PAD WAS APPROX 20 MINS. THAT MEANT THAT WE WERE IN THE DEICING PAD APPROX 45 MINS. I WOULD HAVE CONSIDERED IT AMPLE TIME TO DO A THOROUGH DEICING JOB. WE TOOK OFF IN TOGA PWR WITH ENG ANTI-ICE ON. THE WINDS WERE FROM THE N GUSTING FROM 17-30 KTS. THE RIDE WAS ROUGH WITH LIGHT TO MODERATE TURB THROUGH 10000 FT FOR ABOUT 15-20 MINS AFTER TKOF. JUST AFTER 10000 FT WE WERE STARTLED BY AN ABRUPT AND LOUD VIBRATING NOISE. MOMENTS AFTER THE NOISE; WE NOTICED THE #1 ENG VIBRATION N1 WAS AT 9.9. OBVIOUSLY WE HAD SOMETHING HAPPENING WITH THE #1 ENG. COINCIDENTALLY; ABOUT THE SAME TIME WE WERE GOING THROUGH MODERATE ICING. WE SUBSEQUENTLY ASKED FOR A LEVELOFF AT 16000 FT AND CONSIDERED OUR OPTIONS. AT NO TIME DID WE RECEIVE ANY ECAM WARNINGS. ALL THE OTHER ENG INDICATIONS WERE NORMAL AND IN CONCERT WITH THE #2 ENG. WE EXERCISED THE QRH AND FOLLOWED THE PROCS. THE QRH PROCS DID NOT CALL FOR A SHUTDOWN OF THE ENG. THE FO WENT BACK TO FIRST CLASS TO LOOK AT THE #1 ENG AND SAW A RING OF ICE BUILT UP ON THE ACOUSTICAL TILES INSIDE THE INLET. BY THIS TIME WE WERE ABOUT 100 NM SW OF ZZZ1. WE CALLED ZZZ1 AND ASKED FOR ADVICE FROM MAINT. WE THOUGHT THAT THERE WAS A POSSIBILITY THAT THE ICE BUILDUP WAS CAUSING A BUFFETING ON THE INLET AIR FLOW. AFTER 20 MINS OF TROUBLESHOOTING; THE RECOMMENDATION FROM MAINT WAS TO TAKE THE ACFT TO ZZZ1. THE VIBRATION WAS EVIDENT BUT NOT SEVERE. WE MADE AN OVERWT LNDG IN ZZZ2. UPON INSPECTION OF THE ENG AT THE GATE; WE FOUND THE RING OF ICE WAS MELTING AND 3 LARGE PATCHES OF ICE ON THE INLET BOTTOM FROM 3 INCHES IN DIAMETER TO 6 INCHES IN DIAMETER. THE ICE LOOKED LIKE THE ICE YOU WOULD FIND FROM MELTED SNOW. ALSO; THE INLET FAN BLADES WERE DAMAGED.