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Jeremy Magland Two challenges, each with three strikes at 0, 2 and 4 s; 7 s output d6a9b3f 2 Commits
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challenge.jsonTwo challenges, each with three strikes at 0, 2 and 4 s; 7 s output
README.mdTwo challenges, each with three strikes at 0, 2 and 4 s; 7 s output
README.md

cymbal2-flat-v1: flat annulus struck three times#

The baseline of the cymbal2 tier: a flat annulus of bell bronze with the diameter and the mounting hole of a 16 inch crash and a uniform thickness of 1 mm, struck three times by the stick, at 35 mm from the axis, at half the radius and at 0.85 R, two seconds apart. It has no bow, bell or taper, so every position on it has the same local stiffness, and the three hits differ only through the mode shapes at the strike points; cymbal2-crash-v1 adds the geometry that makes the position matter. The model, the strikes, the listener, the output, the error measures and the common parameters are defined in MODEL.md; this page fixes what is specific to this challenge. The machine-readable version is challenge.json.

Geometry#

Z(r)=0,h(r)=h0,rh≤r≤R.Z(r) = 0, \qquad h(r) = h_0, \qquad r_h \le r \le R.
Symbol Value Unit Meaning
h0h_0 0.001 m thickness
srefs_\text{ref} 16 (provisional) Pa output scale

The lowest elastic frequencies of the annulus in the linear regime are near 22 Hz (two nodal diameters), 38 Hz (axisymmetric) and 51 Hz (three nodal diameters); the hole changes them by less than a percent from those of the full disk. Each stick brings about 1 J and a peak force of a few hundred newtons over about half a millisecond, which bends the annulus by many thicknesses and puts it well into the regime of membrane stiffening.

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