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Jeremy Magland cymbal2: four challenges on one thin-shell cymbal model with a stick strike f723da2 1 Commits
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challenge.jsoncymbal2: four challenges on one thin-shell cymbal model with a stick strike
README.mdcymbal2: four challenges on one thin-shell cymbal model with a stick strike
README.md

cymbal2-flat-v1: flat annulus struck near the rim#

The baseline of the cymbal2 tier: a flat annulus of bell bronze with the diameter, the mounting hole and a uniform thickness of 1 mm, struck by the stick at 0.85 R on the xx axis. It has no bow, bell or taper, so every position on it has the same local stiffness; the three cymbal challenges add the geometry that makes the strike position matter. The model, the strike, 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 and strike#

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
(xs,ys)(x_s, y_s) (0.17272, 0) m strike point, 0.85R0.85 R
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. The 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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