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11.3

New in: | Modified in: | Obsolete in: | Excised in:

11.3

Created by: ruebenko on 03-14-2019 13:00:58

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Bell Acoustics

Georgios Varnavides, Wendi Kong,Monica Shifflet, Emily Thai, Hannah von OldenburgDecember 2016

Introduction

The familiar bell sound is produced by superposition of eigenfrequencies - usually given with respect to the prime (2nd eigenfrequency).

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We can simulate these ‘ideal rations’ inside a decay envelope and produce the following sound.

Model the sounds of a bell.

Clear[sineBank,audioData,sound]primeFrequency=200;ratios={0.5,1,1.2,1.5,2.,2.5,2.667,3,4};decay=Table[If[t<.003,100t,(1-t/4)^3],{t,0,4-1/44100,1/44100}];sineBank["ideal"]=Mean[(AudioGenerator[{"Sin",#},4]&/@(primeFrequencyratios))];audioData["ideal"]=First[AudioData[sineBank["ideal"]]]decay;sound["ideal"]=ListPlay[audioData["ideal"],SampleRate44100,PlayRangeAll]

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Problem statement

There are two convolved effects in bell acoustics. Namely the bell geometry and the material stiffness.Can we reproduce the sound of a bell using arbitrary geometries?In particular holding geometry constant (for an easy to fabricate closed-cap cylinder), can we tune materials properties to achieve an aesthetically pleasing bell sound?Motivation:

Bell casting is a costly process

Traditional bells are usually casted slightly thicker than necessary. They are then turned on a lathe while being tuned simultaneously. This is a wasteful process

Scientific curiosity

Obtaining eigenfrequencies

Importing the bell STL file

Import the geometric model and generate a boundary mesh.

Needs["NDSolve`FEM`"]stlBell=Import[FileNameJoin[{NotebookDirectory[],"SupportFiles","bell.stl"}],"ElementMesh"];

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Visualize the boundary mesh with boundary regions colored.

rr=Most[Range[0,1,1/(Length[stlBell["BoundaryElementMarkerUnion"]])]];colors=ColorData["BrightBands"][#]&/@rr;stlBell["Wireframe"["MeshElementStyle"(Directive[FaceForm[#],EdgeForm[]]&/@colors)]]

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Generate the full mesh.

Cylinder Eigenfrequencies

Materials Properties

Visualize the various material moduli.

Minimization

Experimental Results

Acoustic Comparison

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