One of the reasons for the popularity of cast iron is that it is self damping, so vibrations are rapidly removed by the material.
The science behind "why this happens" is more complicated than this explanation, but basically it comes down to the fact that cast iron is not one, homogenous material, it is a mix of hard clumps and softer adhesive areas. The difference between these materials and how each behaves in relationship to the sound / vibration wave is what makes it damp out quickly.
Epoxy granite mixes share this general concept, which is why they often damp very well.
Al is completely different than cast iron in this way, which is why it rings like a bell. Some Al castings contain so much sand that they start to act a little like cast iron, but most Al material does not.
Steel is somewhere in between, so it depends more on total mass to dampen, then dissipation inside the material. This is why you can fill a steel tube with sand, rubber, or other polymer coatings and it helps more than you might think.
Ger21 tries to make the best of this mixed materials dampening effect by bonding Al and wood laminates together in his builds. He is more patient than most builders though and it appears that he spends at least 1/2 of this time building up layers. That isn't a criticism, just an observation that this approach is labor intensive.
In theory, a composite fiberglass or carbon fiber could be made very stiff, and might actually be able to damp out vibrations very well. One interesting example is the new airbus 380. I have not flown it yet, but my friends that have claim it is MUCH quieter than the Al planes they are used to flying on. That is an indicator of good vibration dampening in a light structure. If you call a many ton vehicle a "light structure".
There is a honeycomb polymer material used in high end boat building known for its vibration dampening. I don't remember the details though, but it is commonly sold down in the Florida area.