So I don't know the answer, but I wanted to get you clued in to be prepared.
Second floor laundry CAN (but not always) come with the shakes. What do I mean? Google it. Turns out that front loaders can be prone to causing house shakes with their high speed spin cycles. It appears that the sub floor can be bolstered (if you knew to do it during the framing stage), you can add "vibration absorbing feet), etc...
Good luck. As I said, I don't have an answer to the fix. It does seem to be washer specific.
Something to consider.