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Jeremy Magland Output: Rayleigh integral of the acceleration with its area mean removed (no baffled monopole from the clamped shell's low modes) 365d2d5 9 Commits
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challenge.jsonOutput: Rayleigh integral of the acceleration with its area mean removed (no baffled monopole from the clamped shell's low modes)
README.mdThe stand as a rigid clamp at the mounting radius (20 mm), replacing the hole and the rigid-motion constraint
scene.jsonThe stand as a rigid clamp at the mounting radius (20 mm), replacing the hole and the rigid-motion constraint
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 of a 16 inch crash and a uniform thickness of 1 mm, clamped at the mounting radius, 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; this page fixes what is specific to this challenge. The machine-readable version is challenge.json.

Geometry#

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

The clamp at the center raises the lowest modes of the free disk (22, 38 and 51 Hz) and turns its rigid motions into elastic ones. 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.

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