Hammered challenge: 150 dents
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5454 | [cymbal-flat-disk-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-flat-disk-v1/README.md) | Flat, free 16 in bronze disk of uniform thickness, Saint Venant-Kirchhoff, struck near the rim by a stick-like pulse | 6 s of radiated pressure |
5555 | [cymbal-bow-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-bow-v1/README.md) | The same disk bowed into a shallow paraboloid (25 mm rise): the effect of curvature alone | 6 s of radiated pressure |
5656 | [cymbal-bell-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-bell-v1/README.md) | The bowed disk with a cosine-dome bell and a mounting hole: the effect of the bell alone | 6 s of radiated pressure |
57-| [cymbal-hammered-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-hammered-v1/README.md) | The belled disk with twenty hammer dents at fixed positions: the effect of breaking the symmetry | 6 s of radiated pressure |
57+| [cymbal-hammered-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-hammered-v1/README.md) | The belled disk with 150 hammer dents at fixed positions: the effect of breaking the symmetry | 6 s of radiated pressure |
5858 | [cymbal-tapered-v1](https://vault1.magland.org/challenges/cymbal/blob/main/challenges/cymbal-tapered-v1/README.md) | The hammered cymbal lathed to a taper (1.2 to 0.7 mm): the effect of the thickness profile | 6 s of radiated pressure |
5959
6060 The string challenge is a hello world: its modal series solution is essentially exact, so it exercises the submission and scoring pipeline and gives a check on the reference rule. The plate challenges define three-dimensional models, so the thin-plate solutions submitted so far (Kirchhoff-Love finite elements for the linear plate, a modal von Kármán method for the nonlinear one) are approximations whose error relative to a future converged three-dimensional solution includes the modeling error of plate theory. Until such a solution arrives, the reference is the best thin-plate solution and the errors measure only differences within plate theory; the results pages say so. The cymbal tier starts from a flat disk and will add the features of a real cymbal one at a time (bell, bow, hammering, varying thickness), each as a new challenge, so that the effect of each on the sound and on the cost of computing it can be seen in isolation; its first solutions are von Kármán modal solutions on Cartesian grids that approximate the disk by a staircase.