How thick is the limit?... never heard anyone say?

Markphd, I think you are wrong when you say "thickness is irrelevant".

Thickness will change the resonant frequency of a mass of wood. I am not saying for better or worse, just that it will change.

Isn't resonant frequency related to mass? More mass=lower Fr.

Also, wood being a 'natural' composit will have the resonant modes distributed so there will not be one 'bell like' peak.
You are correct that speaker builders take advantage of this.
However, a panel of wood used as an enclosure is different that a wood base for a component....for one thing, the pressure stress is applied fairly about all sides, not just the pressure from within an enclosure.

If you seriously want to damp out a wooden shelf, laminate on a sheet of something inert, a very hi density rubber/plastic over a sheet of metal....maybe 3mm of aluminum. Bond it together with a uniformly applied adhesive. Such panels are nearly inert.

Don_s, I will defer to your comment. I will refine mine by saying that thickness is irrelevant to the fact that any material will resonate. Making it thicker or thinner or longer or shorter will not stop it from resonating if you hit the right frequency.

As I understand it from playing the mailing tube and the wine glass, anything will resonate, and at several frequencies from the fundamental up. The exact frequencies depend on the size and composition of the resonating object.

Musical instruments are made to take advantage of these resonances; audio racks, feet, platforms, cabinets et cetera are made to damp them out so they interfere as little as possible with the musical signal.

I suppose it's a losing battle when looked at from a distance, but the near-successes are nice enough that we keep trying.

My experience so far leads me to think that maple platforms are quite successful at damping out resonances when used in a specific way. They have to be sitting on resilient feet and the component on top of them has to be sitting on spikes which contact the wood directly. This is the setup that worked for me.

Yes, everything resonates.
The way to avoid that is to have multiple layers of stuff that doesn't share a frequency. Hi or is that low? hysterisis rubber (whichever one doesn't bounce!) is a good layer to add to a resonant system.
Many years ago, I had a Duel 1209TT. The platter was a 2piece affair. 'Ding' it with a finger nail and it was pretty inert. Take it apart, and each piece rang like a bell.

Look up the Tesla stuff of resonance. He once claimed he could topple the Empire State building with 2 (or 20)HP. Quite a feat.