{
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 "title": "Bowed bronze disk with a bell, a mounting hole and 150 hammer dents, struck with a drum stick, geometrically nonlinear: radiated pressure",
 "generated": "2026-09-17T20:36:16+00:00",
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 "submissions": [
  {
   "schema_version": 1,
   "submission_id": "vonkarman-modal",
   "challenge_id": "cymbal-hammered-v1",
   "submitter": {
    "name": "Jeremy Magland",
    "email": "jmagland@flatironinstitute.org"
   },
   "date": "2026-09-17",
   "description": "Marguerre shallow-shell reduction of the challenge model on a Cartesian grid at 8 mm and 4 mm spacing, as for the bell, with the 150 dents (10 mm radius, 1 mm deep) in the initial shape. The dents break the symmetry in y, so the full modal basis is used: 200 and 400 modes at 8 mm, 400 and 600 at 4 mm. The 8 mm cells barely resolve the dents and stiffen the high modes spuriously (the 400-mode basis reaches 24 kHz at 8 mm against 13.5 kHz at 4 mm), so the 8 mm members should be read as coarse. The hole is closed (a stated approximation); the bell flank exceeds the shallow-shell range; the staircase boundary makes the radiated ring converge only at first order; and the response is chaotic beyond about 0.15 s, so errors between any two solutions have a floor of roughly 0.6 (waveform) and 0.5 (spectrogram).",
   "code_url": "https://vault1.magland.org/challenges/cymbal-solutions/blob/main/solvers/vonkarman-modal-disk/vk_modal_disk.py",
   "viz_url": "https://vault1.magland.org/challenges/cymbal-solutions/site/",
   "key": "cymbal-solutions/vonkarman-modal",
   "source": "cymbal-solutions",
   "source_url": "https://vault1.magland.org/challenges/cymbal-solutions"
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 ]
}