What was found
AIRCRAFT WAS GROUNDED: VIBRATION STARTED ABOVE FL310. INITIALLY NOTED AS A RUMBLE IN 5E FLOOR BOARD THEN FELT IN SEAT. AT FL390, MACH.79 WAS ITS GREATEST INTENSITY. WALKED BACK TO MID CABIN AND COULD STILL BE FELT IN THE FLOOR. DESCENDED TO FL340 AND VIBS PERSISTED (NO WIND,SAT -38 /+14 ISA, TAT -10. L/R ENGINE VIB .3. SLOWED TO .76 AND DEPLOYED SPEED BRAKES TO TEST, NO CHANGE. STILL FELT VIBES AT FL290 AT 290KIAS. LEVEL AT FL240 VIBS ENDED. DECESION MADE TO RETURN TO DFW, AIRCRAFT LANDED WITHOUT INCIDENT. MAINTENANCE REPLACED REPLACED LT WINGLET PER E.A. 377106.