Blame src/presets.ts at 2a1a6da84d692657760321cb869d0255cdb4696a

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago1// Predefined design scripts, selectable from the interface. Each is a

2// MATLAB-syntax script that fills in the `design` struct; see design.ts for

3// the fields. A script is self-contained: the shape functions it uses are

4// ordinary MATLAB functions written at the bottom of the script itself.

6export interface Preset {

7 id: string;

8 label: string;

9 source: string;

10}

12const flatRectangle = `% A flat rectangular sheet of stainless steel, hanging freely (no stand).

13% The script is an ordinary MATLAB program that fills in a struct named

14% design. Lengths are meters; the constants at the top are the only units.

15% A field can be a number or a function handle @(x, y, r, theta) of the

16% point, measured from the center of the bounding box; the handles are

17% applied to whole grid matrices, so use elementwise operators (.*, ./, .^)

18% inside them. Anything else a script needs it defines itself, as MATLAB

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago19% functions at the bottom; the other presets show how. The decay of the

20% sound is not prescribed: it follows from the loss factor of the metal, its

21% thermal constants (thermoelastic damping), the radiation of each mode into

22% the air, and the felt of a stand.

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago23inch = 0.0254; % m

24mm = 1e-3; % m

26design.name = 'Flat steel rectangle';

27design.material.E = 170e9; % Young's modulus [Pa]

28design.material.nu = 0.29; % Poisson ratio

29design.material.rho = 7900; % density [kg/m^3]

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago30design.material.lossFactor = 3e-4; % internal friction of the metal (typical published value)

31design.material.alpha = 17e-6; % thermal expansion [1/K] } for the thermoelastic damping

32design.material.cp = 500; % specific heat [J/(kg K)] }

33design.material.k = 16; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago34design.bounds.width = 12*inch; % bounding box [m]

35design.bounds.height = 18*inch;

36design.thickness = 0.79*mm;

37design.stand = []; % free plate

38`;

76b7843 Slice size follows the bandwidth (about bw/3.5); aluminum square presetJeremy Magland 1 month ago40const aluminumSquare = `% A flat 12 inch square of 6061-T6 aluminum, 1.02 mm thick, with a center

41% hole on a cymbal stand: felt pads below and above the plate around the

42% rod. Aluminum is a third the density of steel and a third as stiff, so

43% the bending frequencies land near those of a steel plate of the same size

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago44% and thickness. Its high thermal expansion and conductivity give it the

45% strongest thermoelastic damping of the three metals here.

76b7843 Slice size follows the bandwidth (about bw/3.5); aluminum square presetJeremy Magland 1 month ago46inch = 0.0254; mm = 1e-3;

47W = 12*inch; hole = 13*mm;

49design.name = 'Aluminum 6061-T6 square';

50design.material.E = 68.9e9; % Young's modulus [Pa]

51design.material.nu = 0.33; % Poisson ratio

52design.material.rho = 2700; % density [kg/m^3]

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago53design.material.lossFactor = 1e-4; % internal friction of the metal (typical published value)

54design.material.alpha = 23.6e-6; % thermal expansion [1/K] } for the thermoelastic damping

55design.material.cp = 896; % specific heat [J/(kg K)] }

56design.material.k = 167; % conductivity [W/(m K)] }

76b7843 Slice size follows the bandwidth (about bw/3.5); aluminum square presetJeremy Magland 1 month ago57design.bounds.width = W;

58design.bounds.height = W;

59design.inside = @(x, y, r, theta) r >= hole/2;

60design.thickness = 1.02*mm;

61design.stand.pad.innerRadius = 7*mm; % the felt sits on the plastic sleeve of the rod

62design.stand.pad.outerRadius = 20*mm;

63design.stand.pad.thickness = 12*mm;

64design.stand.pad.E = 0.5e6; % Pa, felt in compression

65design.stand.pad.lossFactor = 0.3;

66design.stand.topPad = true;

67design.stand.preload = 1*mm; % compression of the top pad by the wing nut

68`;

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago70const bowedRectangle = `% The same steel sheet with a 3 mm parabolic bow across its width, the

71% kind of bow that rolling and handling leave in real sheet metal. The bow

72% makes the sheet a shallow shell: the linear modes couple bending to

73% stretching, and the full simulation oil-cans and wobbles when struck.

74inch = 0.0254; mm = 1e-3;

75W = 12*inch; H = 18*inch;

77design.name = 'Bowed steel rectangle';

78design.material.E = 170e9;

79design.material.nu = 0.29;

80design.material.rho = 7900;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago81design.material.lossFactor = 3e-4; % internal friction of the metal (typical published value)

82design.material.alpha = 17e-6; % thermal expansion [1/K] } for the thermoelastic damping

83design.material.cp = 500; % specific heat [J/(kg K)] }

84design.material.k = 16; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago85design.bounds.width = W;

86design.bounds.height = H;

87design.thickness = 0.79*mm;

88design.profile = @(x, y, r, theta) bow(x, W, 3*mm, 0.3); % stress-free height [m]

89design.stand = [];

91function v = bow(s, span, sag, offset)

92% A parabola of the given sag across a span centered on 0; s runs along the

93% span, and the offset in -1..1 moves the crest toward one end.

94t = 2*s/span;

95v = sag * (1 - t.^2) .* (1 + offset*t);

96end

97`;

99const flatDisc = `% A flat 16 inch bronze disc with a center hole on a cymbal stand. The

100% stand is a rod through the hole with a felt pad below the plate and

101% another above it under the wing nut; each pad is an annulus of felt of

102% the given radii and thickness, and its stiffness per unit area is E over

103% the thickness. The pads hold the disc level and let it bounce and rock.

104inch = 0.0254; mm = 1e-3;

105D = 16*inch; hole = 13*mm;

106

107design.name = 'Flat bronze disc';

108design.material.E = 110e9; % bronze

109design.material.nu = 0.34;

110design.material.rho = 8800;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago111design.material.lossFactor = 2e-4; % internal friction of the metal (typical published value)

112design.material.alpha = 18e-6; % thermal expansion [1/K] } for the thermoelastic damping

113design.material.cp = 370; % specific heat [J/(kg K)] }

114design.material.k = 40; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago115design.bounds.width = D;

116design.bounds.height = D;

117design.inside = @(x, y, r, theta) (r <= D/2) & (r >= hole/2);

118design.thickness = 1.0*mm;

119design.stand.pad.innerRadius = 7*mm; % the felt sits on the plastic sleeve of the rod

120design.stand.pad.outerRadius = 20*mm;

121design.stand.pad.thickness = 12*mm;

122design.stand.pad.E = 0.5e6; % Pa, felt in compression

123design.stand.pad.lossFactor = 0.3;

124design.stand.topPad = true;

125design.stand.preload = 1*mm; % compression of the top pad by the wing nut

126`;

127

128const crash16 = `% A 16 inch flat crash: bronze, lathed to a taper from 1.2 mm at the

129% center to 0.7 mm at the edge, on a stand. Flat, so the linear modes are

130% pure bending modes; the tapered profile is what makes it a crash rather

131% than a ride.

132inch = 0.0254; mm = 1e-3;

133D = 16*inch; R = D/2; hole = 13*mm;

134tCenter = 1.2*mm; tEdge = 0.7*mm;

135

136design.name = '16 inch flat crash';

137design.material.E = 110e9;

138design.material.nu = 0.34;

139design.material.rho = 8800;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago140design.material.lossFactor = 2e-4; % internal friction of the metal (typical published value)

141design.material.alpha = 18e-6; % thermal expansion [1/K] } for the thermoelastic damping

142design.material.cp = 370; % specific heat [J/(kg K)] }

143design.material.k = 40; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago144design.bounds.width = D;

145design.bounds.height = D;

146design.inside = @(x, y, r, theta) (r <= R) & (r >= hole/2);

147design.thickness = @(x, y, r, theta) tCenter + (tEdge - tCenter) * ramp(40*mm, R, r);

148design.stand.pad.innerRadius = 7*mm;

149design.stand.pad.outerRadius = 20*mm;

150design.stand.pad.thickness = 12*mm;

151design.stand.pad.E = 0.5e6;

152design.stand.pad.lossFactor = 0.3;

153design.stand.topPad = true;

154design.stand.preload = 1*mm;

155

156function v = ramp(a, b, x)

157% 0 at x = a, 1 at x = b, clamped to that range outside.

158v = min(max((x - a) ./ (b - a), 0), 1);

159end

160`;

161

162const ride20 = `% A 20 inch flat ride: thicker bronze, 2.2 mm at the center to 1.4 mm at

163% the edge, on a stand with a loose wing nut (a small preload). The

164% thickness raises every frequency in proportion, and the ride has a

165% clearer ping and a longer decay than the crash.

166inch = 0.0254; mm = 1e-3;

167D = 20*inch; R = D/2; hole = 13*mm;

168

169design.name = '20 inch flat ride';

170design.material.E = 110e9;

171design.material.nu = 0.34;

172design.material.rho = 8800;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago173design.material.lossFactor = 2e-4; % internal friction of the metal (typical published value)

174design.material.alpha = 18e-6; % thermal expansion [1/K] } for the thermoelastic damping

175design.material.cp = 370; % specific heat [J/(kg K)] }

176design.material.k = 40; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago177design.bounds.width = D;

178design.bounds.height = D;

179design.inside = @(x, y, r, theta) (r <= R) & (r >= hole/2);

180design.thickness = @(x, y, r, theta) 2.2*mm + (1.4*mm - 2.2*mm) * ramp(50*mm, R, r);

181design.stand.pad.innerRadius = 7*mm;

182design.stand.pad.outerRadius = 22*mm;

183design.stand.pad.thickness = 12*mm;

184design.stand.pad.E = 0.5e6;

185design.stand.pad.lossFactor = 0.3;

186design.stand.topPad = true;

187design.stand.preload = 0.3*mm;

188

189function v = ramp(a, b, x)

190v = min(max((x - a) ./ (b - a), 0), 1);

191end

192`;

193

194const crashBell16 = `% A 16 inch crash with a shallow bow and a cosine bell, on a stand. The

195% profile makes the cymbal a shallow shell: the linear model couples the

196% bending to the stretching (a larger eigenproblem, so the modes take

197% longer), and the full simulation shows the asymmetric nonlinearity of a

198% curved plate. The slopes are kept small; the interface reports the

199% largest one.

200inch = 0.0254; mm = 1e-3;

201D = 16*inch; R = D/2; hole = 13*mm;

202bellR = 55*mm; bellH = 8*mm; bowH = 10*mm;

203tCenter = 1.2*mm; tEdge = 0.7*mm;

204

205design.name = '16 inch crash with bell';

206design.material.E = 110e9;

207design.material.nu = 0.34;

208design.material.rho = 8800;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago209design.material.lossFactor = 2e-4; % internal friction of the metal (typical published value)

210design.material.alpha = 18e-6; % thermal expansion [1/K] } for the thermoelastic damping

211design.material.cp = 370; % specific heat [J/(kg K)] }

212design.material.k = 40; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago213design.bounds.width = D;

214design.bounds.height = D;

215design.inside = @(x, y, r, theta) (r <= R) & (r >= hole/2);

216design.thickness = @(x, y, r, theta) tCenter + (tEdge - tCenter) * ramp(bellR, R, r);

217design.profile = @(x, y, r, theta) bowH * (1 - (r/R).^2) + dome(r, bellR, bellH);

218design.stand.pad.innerRadius = 7*mm;

219design.stand.pad.outerRadius = 20*mm;

220design.stand.pad.thickness = 12*mm;

221design.stand.pad.E = 0.5e6;

222design.stand.pad.lossFactor = 0.3;

223design.stand.topPad = true;

224design.stand.preload = 1*mm;

225

226function v = ramp(a, b, x)

227v = min(max((x - a) ./ (b - a), 0), 1);

228end

229

230function v = dome(d, radius, height)

231% A cosine dome of the given height and base radius, with zero slope both at

232% its rim and at its apex; d is the distance from its center.

233v = 0.5 * height * (1 + cos(pi * d / radius)) .* (d < radius);

234end

235`;

236

237const ellipse = `% A free elliptical steel plate. The outline is any test on the point;

238% an ellipse inscribed in the bounding box here. The degenerate mode pairs

239% of a disc split on an ellipse, which the mode browser shows.

240inch = 0.0254; mm = 1e-3;

241A = 14*inch; B = 10*inch;

242

243design.name = 'Steel ellipse';

244design.material.E = 170e9;

245design.material.nu = 0.29;

246design.material.rho = 7900;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago247design.material.lossFactor = 3e-4; % internal friction of the metal (typical published value)

248design.material.alpha = 17e-6; % thermal expansion [1/K] } for the thermoelastic damping

249design.material.cp = 500; % specific heat [J/(kg K)] }

250design.material.k = 16; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago251design.bounds.width = A;

252design.bounds.height = B;

253design.inside = @(x, y, r, theta) (x/(A/2)).^2 + (y/(B/2)).^2 <= 1;

254design.thickness = 1.0*mm;

255design.stand = [];

256`;

257

258const thunderSheet = `% A thunder sheet: a large thin steel sheet hung from one corner. Its modes

259% are dense and low, and the full simulation turns a hard hit into a roar.

260% Long at the default spacing; a coarser grid keeps it interactive.

261inch = 0.0254; mm = 1e-3;

262

263design.name = 'Thunder sheet';

264design.material.E = 200e9;

265design.material.nu = 0.3;

266design.material.rho = 7850;

2a1a6da Derive the losses from physical constants instead of a prescribed decay curveJeremy Magland 1 month ago267design.material.lossFactor = 3e-4; % internal friction of the metal (typical published value)

268design.material.alpha = 12e-6; % thermal expansion [1/K] } for the thermoelastic damping

269design.material.cp = 460; % specific heat [J/(kg K)] }

270design.material.k = 50; % conductivity [W/(m K)] }

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago271design.bounds.width = 24*inch;

272design.bounds.height = 36*inch;

273design.thickness = 0.5*mm;

274design.stand = [];

275`;

276

277export const PRESETS: Preset[] = [

278 { id: "flat-rectangle", label: "Flat steel rectangle", source: flatRectangle },

76b7843 Slice size follows the bandwidth (about bw/3.5); aluminum square presetJeremy Magland 1 month ago279 { id: "aluminum-square", label: "Aluminum 6061-T6 square on a stand", source: aluminumSquare },

5778036 cymbalsim: scripted plate and cymbal designer with a modal linear model and a von Karman GPU modelJeremy Magland 1 month ago280 { id: "bowed-rectangle", label: "Bowed steel rectangle", source: bowedRectangle },

281 { id: "flat-disc", label: "Flat bronze disc on a stand", source: flatDisc },

282 { id: "crash-16", label: "16 inch flat crash", source: crash16 },

283 { id: "ride-20", label: "20 inch flat ride", source: ride20 },

284 { id: "crash-bell-16", label: "16 inch crash with bell", source: crashBell16 },

285 { id: "ellipse", label: "Steel ellipse", source: ellipse },

286 { id: "thunder-sheet", label: "Thunder sheet", source: thunderSheet },

287];

288

289export const DEFAULT_PRESET = "crash-16";

290

291export function presetById(id: string): Preset | undefined {

292 return PRESETS.find((p) => p.id === id);

293}