How to isolated stand from springy floors?

I currently have a relatively heaving stand with a couple tube amps and a turntable on it. My big issue isn't really sound quality but my concern over tube life. My Manely Stringray II makes an audible tube rattling sound when ever my fairly light self walks by and I hoping I can come up with a fairly simple and hopefully cheap solution to this.

What would you guys suggest? Damping the underside of the shelf the amp is on comes to mind or possibly some sort of iso feet for the whole rack to cut down on vibration.
Herbies tube rings on all tubes in preamp and Symposium Utra under preamp.
Use Symposium HDSE feet between shelf and preamp as well.Enjoy!!
Thanks for the quick response man. I haven't really looked much into tube rings/dampeners, do they alter sound much?
Usually bad tubes are more sensitive to mechanical disturbance.
Foot fall vibration on a sprung floor is tough to eliminate. Use a wall shelf rack attached to a load bearing wall will help isolate your equipment off the floor and away from foot fall vibration.
Regarding tube damper rings on small tubes found in preamps, I have noticed tighter bass and reduction in microphonics from airbourne sound waves.
Mass on a spring isolation. Like the pros use.
More mass. Add a few hundred pounds of mass around under the rack. Bricks will do. Get heavy ones. Concrete like.
I concur with Elizabeth, but suggest using dumb-bells instead of bricks since they are relatively easy to find and install. They also provide a more effective way to accumulate mass compared to bricks.

The ones to look for are Hex-Shaped with a Rubberized Covering. 4 50-lbs bells arranged in parallel, with a 1/4 or 1/2 inch Marble Tile placed on top should provide a fairly even surface to put your stand.
If you can access the subfloor, put cross joists or sister some additional joists onto the existing floor joists.

It sounds a lot harder than it actually is.
If you have access to the basement and it is un finished, you could put in some "lally columns" see link
I did this when I had an LP12 to reduce the springy response to footfall. Locate the two joists that your equipment rack is supported by and tighten the lally columns to just touch the joist. Then the solid cement floor is transferred through the columns and acts like a foundation to support the floor.
Caution though, if you have expansive soil in your area this will not work.
Another partial solution if you have access is to add "bridging" between the joists. This is a board that fills that gap in a perpendicular position to reduce the flexing that takes place when a joist deflects from load.

As a final note, and not to argue with Elizebeth, but I think adding weight will just prove to further damage to the floor and cause more issues down the road. But that is just my opinion and I am not an engineer.
What Theo mentions about supplementary posts is a good call if possible, because it's likely the most effective. Bridging will help as an alternative, but along similar lines would be to sister additional joists on either side of the joists where the load lies. Even if you basement is finished, this is not a hard job and cosmetically we're talking some drywall work and paint (both cheap). Of course, if you have wiring / plumbing through existing jiosts, that does add complication.
A floor should be able to hold furniture and other heavy and heavier items than just loads of send-boxes recommended by Elizabeth. Further damage will continue to the unloaded springy floor that needs to be damped.
Like the additional joist idea (sister). Use adhesive as well as nails or screws.
You could also box the joists (every other pair) with 1/2" or 3/4" plywood, again using adhesive and nails or screws.

Either of these choices should stiffen the floor considerably. The adhesive is important. Both ideas requires floor to be open underneath.
From your pic it looks like hardwood, IOW a floating floor, so how are tighting up the joists of the subfloor going to help? There will still be some "spring" in the floor.
Even with mass loading, there will still be some bounce. The floor needs to be damped, with the addition of isolation footers under the component and if possible, isolation under the shelf.

Also IME, do not put any iso feet under the rack; it is likely to affect the performance of your TT. I'll bet your TT is very happy being on a heavy stand touching the floor.
As a quick effort at low cost, what I have done is beneath those components where there is no interposed individual maple board base supporting the component, simply place three or four Cryo'ed Mini Springs between the component and the existing hard, flat base.
Even though some of your components may quiver when you walk by, there won't be a jarring shock to any of the protected components.
The sound you hear from your suspended components will surprise you with the improvement heard.
Long ago, the Aurios ball bearing approach also allowed for this quivering or rocking when footfalls affected components on my equipment stand, but the sound improvement was nowhere near the significant upgrade with the Mini Springs from Machina Dynamica.
There are variations in implementing these springs.
This minimalist approach is fast, simple, audibly impressive -- even though not the "ultimate" implementation of what is termed Baby Promethean Mini Isolators by Machina Dynamica.
The entire house is moving. So making the floor rigid will not solve the underlying problem. The ideal solution would be to isolate the house and the components.
Interestingly, the OP makes no mention of problems (skipping, feedback) with the turntable; in fact, he suggested that there is no issue with the sound. The turntable, while it has a type of suspension (rubber feet between the chassis and plinth) and is generally very good, is not known for being particularly immune to this sort of problem. If the floor were truly "springy" this would affect turntable playback. Before undertaking more drastic fixes, I would look for an extremely microphonic tube in the amplifier; replacing each tube one at a time to isolate the culprit(s) and also putting some isolation device under the amp. I would suggest that the problem is not floor springiness but a tube or an amp that does not have good immunity to low frequency excitation; something that would probably not be solved by adding mass underneath it and, in fact, could make the problem worse.
04-09-14: Czarivey
Usually bad tubes are more sensitive to mechanical disturbance.

04-11-14: Frogman
Before undertaking more drastic fixes, I would look for an extremely microphonic tube in the amplifier; replacing each tube one at a time to isolate the culprit(s) and also putting some isolation device under the amp.
Among the many comments that have been made I particularly second these. I'll add that another way of determining if a tube is excessively microphonic is by LIGHTLY tapping each tube with a pencil eraser, while the amp is powered up but no music is playing, and seeing (i.e., hearing) what happens.

-- Al
Thanks for all the advice, I have been trying out few different variations and I think I might have this worked out.

Since I posted this I have changed my TT to a Garrard 301 with a very heavy plinth and I also purchased some of Herbie's big dot gliders to go under the whole rack. I think between the extra weight on top of the rack and the dampening feet I have found a pretty good balance. It could have been that my rack was simply just a bit to light in the beginning and the extra mass has fixed this issue.

After my success with the initial change I got some of herbie's SS dampening rings for my pre tubes and I still haven't really decided if I like the way they changed the sound. They give everything a bit of a thinner feel and have removed a bit of the romantic/lush sound my system used to project. That all said they do do pretty much exactly what they claim; tighter bass, cleaner highs, and a bit of a sound stage bump.