Longest ringing/resonating object I am interested in objects which resonate or ring for as long as possible. In particular, I am interested in Crotales (https://en.wikipedia.org/wiki/Crotales), and if it is possible to make a longer ringing version DIY. I would really like to hear suggestions/comments about the physics involved here!
I guess the three important parameters here are 1) material 2) shape 3) manufacture process.


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*Material. Many percussion instruments are made of bronze or brass. Are these the best materials? Or is there another metal which will do as well.

*It seems that the two most used shapes are either flat plates/circle (e.g. thundersheets or crotales) or bell shapes. I am told that the increasing diameter of bells creates standing waves of decreasing frequency around the perimeter of the bell. However, I am mostly interested in a flat objects.

*I made a DIY cymbal out of a circular very thin steel sheet. However, it hardly resonated at all. Do rims (either outside or in the center) create more resonance? Would stretching the metal in some way help it to resonate?
 A: 0) Try to get the book "The physic of musical instruments" by Fletcher and Rossing. It has almost everything you may need clearly explained.


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*Material, you want one with low internal damping, that mean, low internal wasting of energy.  The damping coefficient varies a lot between metals alloys and treatments. Bronze is among the best; soft steel is quite bad. Have a look at the tables in this paper, you want small $\eta$. If you can afford, go for pure platinum!

*Two things about the shape: first, the thicker and heavier, the more energy can store, so the longer resonation. Also, thin flat produce a lot of sound, so decay faster. Large (10+ tons) bells can sound for minutes. You can keep the same tone in a larger crotal by making it proportionally much thicker. Second, shape: that is difficult, as current instruments have been empirically refined to have optimal shape; it depends on how they vibrate, and they do that in really strange ways.  Best sustain, from my experience, diapason, triangle, western bronze bells. You won't get much from a flat disk. (Edit: after @alephzero answer, I looked at crotales, they last long! so maybe disk is good)

*The thinnest, the shorter it resonate; and soft steel is a bad material. This may explain your result. Rims, who knows, they surely affect vibration but must be "perfectly sized" with trial and errors to get good results. Hammering/stretching may work a little. Best for steel, is to quench it hard; but bronze will be better.


So, I would try with a thick disk of bronze or aluminium. Or if you can find a thick slice of semiconductor-grade silicon.
Another importaint factor, how the crotal is suspended: wrong mounting can mute the best bell.
A: The "unique" feature of the design of crotales is the relatively big solid central cylinder, which faces down when playing them, and therefore isn't easily visible.
That is much more rigid than the mounting of a typical drumkit cymbal, so all the internal energy in the crotale gets converted (slowly) into sound, rather than wasting energy shaking its support.
Compared with "normal" cymbals made from coiled wire, the plate of the crotale is rigid and relatively thick. The material is usually bronze. 
If you don't know a percussionist (or musical instrument shop) who would let you measure one, you can get a fair idea of the actual shape of crotales and how they are supported when playing from this video: https://www.youtube.com/watch?v=e3_MlMJ1bP0.
