What was found
AIRCRAFT WAS GROUNDED: AN EMERGENCY WAS DECLARED AND THE AIRCRAFT TO SEA. CLIMBING THROUGH 17000', 340 KNOTS FLIGHT ATTENDANT CALLED AND INDICATED LOUD LOW MECHANICAL RUMBLING. METAL GRINDING, CARTS AIRCRAFT RIGHT VIBRATING AND THE LEFT SIDE STATIONARY. THEY COULD FEEL VIBRATION IN TOUCHING FLOOR WHEN NEAR DOOR. FLIGHT CREW LEVELED OFF AT FL 210 AND VIBRATION DISSIPATED.VIBRATION RETURNED UPON PITCH/ POWER CHANGES FOR CLIMBS AND DESCENTS. THE AIRCRAFT LANDED SAFELY AT SEA WITHOUT FURTHER INCIDENT. MAINTENANCE FOUND THE R4 DOOR UPPER COVER PLATE OUT OF ADJUSTMENT AND ADJUSTED IT PER AMM 52-10-00-220-007-A.