A B737-400 ON LEVEL OFF AT FL350 DECLARED AN EMER AND DIVERTED DUE TO EXCESSIVE AND SEVERE AIRFRAME VIBRATION CAUSED BY A FAILED ELEVATOR TAB.

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I WAS THE CAPT ON ACR X FLT XXXX FROM ZZZ; FO TO ZZZ; US. WE EXPERIENCED EXCESSIVE VIBRATION ENROUTE. IT STARTED WHEN WE WERE CLBING OUT OF ZZZ; FO; BUT IT WAS NO WORSE THAN IT WAS ON THE WAY DOWN; AND 2 DAYS BEFORE WHEN I FLEW THAT AIRPLANE. WE WERE GOING THROUGH ABOUT FL200 AND THE VIBRATION COMPLETELY STOPPED. THE VIBRATION CAME BACK ABOUT 10-15 MINS LATER AS WE WERE LEVELING OFF AT FL350. IT GOT CONSIDERABLY WORSE; BUT UNTIL THEN I WAS NOT CONCERNED. WE TRIED BRINGING THE POWER BACK ON BOTH ENGS; ONE AT A TIME OF COURSE. NO DIFFERENCE. WE TRIED SLOWING DOWN; THAT MADE A LITTLE BIT OF DIFFERENCE; BUT NOT MUCH. AT THAT TIME I REALIZED THERE WAS SOMETHING STICKING OUT IN THE AIRFLOW THAT SHOULDN'T BE THERE. ABOUT THAT TIME THE LEAD FA CAME UP AND SAID THE PANELS IN THE BACK WERE FALLING DOWN. I SENT THE FO BACK TO TAKE A LOOK. HE CAME BACK UP FRONT AND SAID THE VIBRATION WAS MUCH WORSE IN THE BACK. AT THAT TIME I DECIDED WE MUST LAND. BY THIS TIME WE WERE ALMOST OVER ZZZ2 FO. WE DIDN'T HAVE ANY CHARTS FOR ZZZ2 FO AND I DIDN'T THINK WE WOULD BE WELCOME THERE; SO THE CHOICES WERE TO GO BACK TO ZZZ FO OR TO ZZZ1 US WE DECIDED ON ZZZ1 US SINCE IT HAS LONGER RWYS (SINCE WE WERE DOING AN OVERWT LNDG) AND BETTER EMER EQUIP (WE DIDN'T KNOW HOW BAD THE VIBRATION WAS GOING TO GET). WE SLOWED TO 250 KNOTS EARLY; AND FLEW AT THAT SPEED ALL THE WAY INTO ZZZ1 US. AS WE WERE ADDING FLAPS '5' THE VIBRATION STOPPED. WE WENT BACK TO FLAPS '1'; AND THE VIBRATION STILL WASN'T THERE. SO AT THAT TIME I THOUGHT IT WAS A FLAP PROB. WE CONTINUED TO ADD THE FLAPS UNTIL FINAL FLAPS '30'; AND LANDED NORMALLY. THE TRUCKS WERE WAITING FOR US; BUT WE TOLD THE CTLRS WE WERE FINE; AND TAXIED INTO THE GATE NORMALLY. ON POST FLT WALK AROUND; I NOTICED HALF OF THE BALANCE TAB ON THE ELEVATOR WAS MISSING. MY OPINION IS THAT IT LEFT THE AIRPLANE WHEN WE WENT FLAPS '5'. I ALERTED MAINT AND WENT TO THE HOTEL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE VIBRATION WAS NOTED IN THE COCKPIT AND DID APPEAR EXCESSIVE UNTIL THE RPT FROM THE LEAD CAB ATTENDANT OF CEILING PANELS FALLING DOWN. THE RPTR SAID THE DECISION WAS MADE TO DECLARE AN EMER AND DIVERT AND THE VIBRATION WAS LIMITED IN INTENSITY WHEN THE AIRPLANE WAS SLOWED TO 250 KNOTS. THE RPTR STATED THE LNDG WAS UNEVENTFUL. THE RPTR SAID THE MAINT RPT INDICATED THE FAILURE WAS CAUSED BY THE ELEVATOR TAB BEARINGS WHICH HAD 1000 HRS OF SVC AFTER THE REQUIRED 2000 HR CHK.