If you build the stand properly it will be rock solid. If it has "shake" it wasn't safe from the get go. When you build stands like the one in my picture they have no movement in them at all with or without a tank on them. I use 3" screws and it would take a richter 9 earthquake to make the screws come out.
ive built tons of stands. and i used the same exact build your is like. But this stand will be different. I just finished building the frames. I just cut the Legs, now i just need to cut out the supports and I should be done.
An issue i have right now is finding good wood :/ all the wood at my local hardware store *lowes) is crap. They are all bend and warped. i tried finding the best wood i could but they are still a little warped. But im going to try to just bend them a bit to make the straight. My build is going to be UrauJoey's Large multiple tank build.
I'll post pictures later on. Now I just have to pick up the second tank and drill it.