You are on the right track to decouple the bed from the floor in terms of low frequency vibrations, by combining weight with absorption.
Heavy machines and sensitive audio turntables also use the combination of added weight and absorptive material in legs or bushings. Also foot-drop noise from "upstairs people" is combatted with extra weight in the subfloor.
Since you are DIY-ing this, you have allowance for experimentation and you can improve your design over time. This will be key.
Remember that your own weight also counts towards dampening. So the weight of such concrete posts must be more than your weight to make a difference.
The concrete post does not have to be tall, it can be wide, almost like placing your bed's leg on a small concrete slab. The point is to have weight, so pouring your own legs is fine. Do not using low-weight "aerated" concrete bricks. You can add a few clean river rocks to the mix, to add volume for free and help reduce cost. The compressive strength will be sufficient if the pad is a few inches thick, and it will allow for gymnastic activity.
To have a thick concrete pad without raising the bed too much, you could leave a "cup holder" cavity for the bed's leg. Just make sure the remaining concrete thickness right under the leg is still at least a few inches, and that of course the bed frame still fits over the rim of such a concrete form. Forming can be done with buckets and yoghurt containers or scrap lumber.
For dampening you can use cork mats, cut to the size of the concrete leg, and applied in several layers under the concrete. Cork comes in different price categories. As a yoga mat it's likely at its priciest per square foot, and you don't need tongue in groove flooring tiles. Look at cork boards in office supply stores.
A concrete pad that's 12in x 12in would probably suffice to spare the cork from over compression. On-line concrete calculators can help you determine how much you need based on the dimensions, and how much it will weigh.
As you have probably seen already, "anti-vibration" pads exists and they are quite pricy and quite small (4in x 4in). The ones for washing machines are designed for durability under mechanical stress (weight & movement), and water resistance. The ones for audio are designed for aesthetics and profits. Your DIY solution will likely be much better, plus you can experiment with it.
As for overall size and calculations, this would have be analyzed in a computer model. Or you may be lucky to find a research paper or thesis on this topic, and be able to use graphs or tables. Or you can experiment, and then write an article or create a youtube video to journal your experience! For measurements one would need specialized sensitive low-frequency microphones or accelerometers coupled to the bed. A "sound level" cell-phone app with spectrum analyzer looks cool but is really not useful for this.
Ideally you would be looking at about 60 to 80dB of attenuation to get rid of it. It's amazing how well we hear when we are trying to fall asleep, all quiet in bed, and are bothered by even the faintest noise of thumps, cracks and buzzes.
As an alternative you could hang the bed from the ceiling, provided upstairs produces less thumping...
Image:
