plate-strike-nl-v1: soft mallet strike, 40 N over 5 ms
2 changed files+8−8
challenges/plate-strike-nl-v1/README.mdmodified+4−4View file
@@ -1,6 +1,6 @@
11 # plate-strike-nl-v1: hard-struck free aluminum plate, geometrically nonlinear
22
3-This challenge is [plate-strike-v1](../plate-strike-v1/README.md) with one change in the model and one in the strike. The plate is the same free 12 in by 12 in by 1.04 mm aluminum plate with the same damping constants, but the material is a Saint Venant-Kirchhoff hyperelastic solid, so that strain is measured exactly and stress acts on the deformed configuration, and the strike carries a hundred times the impulse. The material remains elastic; the nonlinearity is purely geometric. It is what produces the sound of a gong or a cymbal when struck hard: a downward pitch glide of the low partials as the amplitude decays, and a cascade of energy from the struck modes into a broadband wash. The strike here is chosen so that the transverse displacement predicted by the linear model would be many times the plate thickness, deep in the regime where these effects are unmistakable.
3+This challenge is [plate-strike-v1](../plate-strike-v1/README.md) with one change in the model and one in the strike. The plate is the same free 12 in by 12 in by 1.04 mm aluminum plate with the same damping constants, but the material is a Saint Venant-Kirchhoff hyperelastic solid, so that strain is measured exactly and stress acts on the deformed configuration, and the strike is a soft mallet blow with forty times the impulse. The material remains elastic; the nonlinearity is purely geometric. It is what produces the sound of a gong or a cymbal when struck hard: a downward pitch glide of the low partials as the amplitude decays, and a cascade of energy from the struck modes into a broadband wash. The strike here is chosen so that the transverse displacement predicted by the linear model would be many times the plate thickness, deep in the regime where these effects are unmistakable.
44
55 The deliverable, listener geometry, error measures, and optional field export are identical to plate-strike-v1, except for the duration and scale stated below. The machine-readable version of this specification is [challenge.json](challenge.json).
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@@ -41,10 +41,10 @@ All parameters are those of plate-strike-v1 except the peak force and the durati
4141
4242 | Symbol | Value | Unit | Meaning |
4343 | --- | --- | --- | --- |
44-| $F_{\max}$ | 250 | N | peak total force of the strike |
45-| $T_s$ | 0.002 | s | strike duration |
44+| $F_{\max}$ | 40 | N | peak total force of the strike |
45+| $T_s$ | 0.005 | s | strike duration |
4646
47-The impulse is $F_{\max} T_s / 2 = 0.25$ N s, that of a mallet rather than a drumstick. For comparison, the 10 N, 0.5 ms tap of plate-strike-v1 carries 0.0025 N s and bends the plate by only a few hundredths of a millimeter (the several millimeters visible in its field export are rigid-body drift); a linear extrapolation of that response to the present impulse gives a bending amplitude of several millimeters, several times the thickness, which the nonlinear model limits by membrane stiffening. The longer pulse feeds mainly the modes below about 1 kHz, so the high-frequency content of the sound is produced by the nonlinear cascade rather than by the strike itself, as in a gong. The plate is free, so the impulse also sets it drifting at about 1 m/s; this rigid motion carries no acceleration after the strike and does not enter the output, but it dominates the raw displacement in the field export, and a viewer will want to remove the best-fit rigid motion from each frame.
47+The impulse is $F_{\max} T_s / 2 = 0.1$ N s, forty times that of the 10 N, 0.5 ms tap of plate-strike-v1, and the contact is ten times longer: a soft mallet rather than a stick. That tap bends the plate by only a few hundredths of a millimeter (the several millimeters visible in its field export are rigid-body drift); the present strike bends it by about four thicknesses, where membrane stiffening is strong. The 5 ms pulse feeds mainly the modes below a few hundred hertz, so the high-frequency content of the sound is produced by the nonlinear cascade rather than by the strike itself, as in a gong struck with a soft beater. Harder strikes of the same plate were tried and sound like a slammed sheet of metal rather than an instrument. The plate is free, so the impulse also sets it drifting at about 0.4 m/s; this rigid motion carries no acceleration after the strike and does not enter the output, but it dominates the raw displacement in the field export, and a viewer will want to remove the best-fit rigid motion from each frame.
4848
4949 ## Output signal
5050
challenges/plate-strike-nl-v1/challenge.jsonmodified+4−4View file
@@ -10,10 +10,10 @@
1010 "sample_format": "float32",
1111 "signal": "acoustic pressure at the listener point from the Rayleigh integral over the top face",
1212 "signal_unit": "Pa",
13- "signal_scale": 64.0
13+ "signal_scale": 10.0
1414 },
1515 "playback": {
16- "gain_db": 24,
16+ "gain_db": 36,
1717 "note": "Suggested playback gain for listening; presentation only, not part of the deliverable."
1818 },
1919 "parameters": {
@@ -28,8 +28,8 @@
2828 "strike_x": 0.09144,
2929 "strike_y": 0.10668,
3030 "strike_radius": 0.01,
31- "strike_duration": 0.002,
32- "strike_peak_force": 250.0,
31+ "strike_duration": 0.005,
32+ "strike_peak_force": 40.0,
3333 "rho_air": 1.204,
3434 "c_air": 343.0,
3535 "listener_x": 0.2524,