I made a Simulation with COMSOL for the Yend table. Mainly, I tried to see how the lower eigenmode changes with the number and the size of the posts inside.

The lateral frame is just sitting on the table, it is fixed by its weight. I also put a couple of screws to fix it better, but the resulting eigenfrequency didn't change so much (less than 1 Hz). 

In Fig. 1 I didn't put any post. Of course, the lowest eigenfrequency is very low (around 80 Hz).

Then I added 2 posts, one per side (Fig. 2 and Fig. 3), with different diameter.

In some cases posts don't have a base, but they are fixed to the table only by a screw. It is just a condition to keep them fixed to the table

Eventually I put 4 posts, 2 per side. 

The lowest eigenfrequency is always increasing.

At the end I also put a simulation for 4 1.6 inch diameter posts without base, and the eigenfrequency is slightly higher. I want to check it again, because I would expect that the configuration shown in Fig.5a could be more stable.

P.S.: All the post are stainless steel.