The fencing company had no ideas at all.
I would really appreciate some suggestions on dampening the vibration in a way that still allows the gate to open.
The construction of the gate is powder coated vertical steel tubes in a box section frame. It's bolted onto concrete (not attached to the house)
I've isolated the vibration to a couple of the vertical tubes. I tried clamping rubber clamps onto a tube, but that didn't work. Leaning a big lump of wood against the gate does, but makes it a pain to open/close the gate.
I thought about filling the tubes with expanding foam, but that requires holes so risks rust.