d6a9b3fTwo challenges, each with three strikes at 0, 2 and 4 s; 7 s outputJeremy Magland 1# cymbal2-flat-v1: flat annulus struck three times
d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 3The 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 45, 120 and 185 mm from the axis, 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](../../MODEL.md); this page fixes what is specific to this challenge. The machine-readable version is [challenge.json](challenge.json).
d6a9b3fTwo challenges, each with three strikes at 0, 2 and 4 s; 7 s outputJeremy Magland 5## Geometry
7$$
8Z(r) = 0, \qquad h(r) = h_0, \qquad r_h \le r \le R.
9$$
11| Symbol | Value | Unit | Meaning |
12| --- | --- | --- | --- |
13| $h_0$ | 0.001 | m | thickness |
14| $s_\text{ref}$ | 16 (provisional) | Pa | output scale |
d7c7d17Realistic crash: plate-synthesis losses (sigma1 Laplacian term, small eta), firm 6 m/s stroke, rim 0.65 mm, strikes on the bell flank, the bow and the thin edgeJeremy Magland 16The 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 0.36 J and a peak force of several hundred newtons over about a millisecond, which bends the annulus by several thicknesses and puts it into the regime of membrane stiffening.