There is some tech behind it... here's some you'd consider for a more demanding situation so you can see what I'm on about:
Mass is important in anti-vibration.
If using rubber, the type of rubber is important.
Calculations revolve around coupling, cutoff frequencies, characteristic resonances and hysteresis losses.
If say you're sitting a fan/pump on the joists, you need to reduce the amount the fan/pump moves, so fix it to a paving slab to increase the mass, so it moves less. A padstone is more dense but more cost per kg.
Then the support between that and the joists needs to be as squishy as possible - ideally something like an air bag, so the coupling of the movement to the joist is as weak as possible. Air bags are rarely practical, but are used where they can be maintained. (e.g. a whole tyre inner tube, partially inflated). You can use a lot of soft metal springs, but they aren't very lossy.
Increasing the mass increases the coupling, but there are square laws etc in there so mass increase is still good - you need more spreading of support- intuitive, really.
Ordinary rubber doesn't have much hysteresis - in other words the energy you put in to squash it is stored, and is given back when you release. No good. Something like Sorbothane (see ebay) is designed to not do that, but heat up slightly to absorb the energy. It's used on optical equipment etc. You need to look at their tables to pick the right shape/volume of foot for the mass and frequency (rpm for a fan).
I've used that in other circumstances.
Salamander and Manrose and Stuart Turner sell or recommend particular feet, but they aren't great, I've tried that.
Bungees off the rafters would be pretty good, until the rubber in them perishes. Haven't tried that.
Rolls of old carpet aren't bad as long as there's enough of it. I've used that. It tends to settle into a hardish lump. Cheap pipe insulation lasts a week... ditto!
Non-rotting foams like Dunlopillow aren't bad. I've used that.
Ideally, a bit of something like old shelf - melamine faced chip board, to sit the fan on with a brick, 3 or 4 of those Sorbothane feet on to another bit of old shelf resting across rafters, and you have negligible structural transmission, the stuff is that good. You might still hear the motor of course.