What causes metallic objects to ring?
Whether something rings when struck depends on the mechanical properties of the bulk material. Ringing depends on the ability of the bulk material to recover from a mechanical impact elastically with little loss of energy. That way the block of material can vibrate for a significant period of time and we hear this because of the interaction of these vibrations with air, creating sound.

The bulk properties of a material depend on both the nature of the material and the crystal structure of the bulk solid. Ringing doesn't happen if the material has ways of dissipating mechanical energy quickly rather than by vibrating elastically. This can be because of a low elasticity but also because the crystal boundaries may create ways to dissipate energy.

So some metals don't ring. Lead makes very bad bells (as does mercury when solid as demonstrated in this amusing video). Many polymers don't ring as they have many internal ways to dissipate vibrational energy quickly. But many elastic materials like brass, iron or glass do ring because they don't have any easy internal ways to absorb vibrational energy.