In a word: No.
That is why I used a non-hardening glue in a 2 mm thickness. Remember, there is a lot of glue underneath.
There are no free-hanging, undampened metal hanging around to vibrate.
The weight of each sub has increased from around 50 kilos to 70 kilos.
Before adding the metal sheet, I could easily feel the frame vibrating when playing at louder volumes.
Now, not so much.
The main speaker is inspired by Dannys Line Force speaker, and it _does_ have an unbraced area, the wing:
It is constructed much the same way. Drivers are mounted in a 30 mm birch ply sheet, which is glued (again 2 mm layer) to a 4 mm steel frame.
The drivers only play from ~250 Hz, so there is not a lot of kinetic energy, compared to the subs.
I do not experience any ringing, but future tweaking could be damping of the wing.
Have a nice weekend.