I'm judging from the video another comment above posted. But it seems to me, that if the vessel is at or close to atmospheric pressure that from most measures

I'm judging from the video another comment above posted. But it seems to me, that if the vessel is at or close to atmospheric pressure that from most measures it should be unchanged. The gas below the 'floating' liquid is at an increased pressure due to the weight of the liquid, and the gas above my be at a somewhat reduced pressure. But since the floating liquid has reached a stable point the pressure in the liquid should be much the same as it would be in normal conditions relative to the local atmospheric pressure. I can't imagine how shaking would affect that signficantly. Regarding the shaking, anything in the liquid should receive a significantly dampened shaking and would likely acclimate. This is at best armchair theorization on my part of course.