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

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.

Why not tap the tubes gently with a pencil (top part with the eraser - don't break your tube!) and see you if you can hear anything out the speakers (with the amp on of course) - if you hear nothing then you have saved yourself a lot of worry!

Thanks to all who answered. I am begining to think the mass is not terribly relevant. I have two independeant needs. The shelf to isolate the TT from the floor which will require some serious decoupling and isolation of some type and the Amp stands. The Amp stands are more or less just mass dampening even if it resonates it will take some energy to do so at 4 inches thick. As I said I just wanted to know if there was a real detriment which did recieve the knod from one post. Otherwise these cool looking wood platforms will be ready to grace the dedicateed listening and audio storage facility shortly.