"I don't remember where and when but my mind reminds me of a publication in which airbus was saying that was going to programme the autotrim of the airbus to give a slight nose down input so that the elevator, the part of the tail where the 90% of the vibrations come from, was always under a constant load and it would not vibrate. At least this is what comes in my mind..
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bio161 you are correct. My company which has a very large Airbus fleet, did an intensive investigation with Airbus and this was the corrective action. Little vibration problems since.