dorsal/arxiv
View SchemaContribution to harmonic balance calculations of periodic oscillation for self-sustained musical instruments with focus on single-reed instruments
| Authors | Snorre Farner, Christophe Vergez, Jean Kergomard, Aude Lizée |
|---|---|
| Categories | |
| ArXiv ID | physics/0503047 |
| URL | https://arxiv.org/abs/physics/0503047 |
| DOI | 10.1121/1.2166602 |
Abstract
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has later been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying every periodic solution of the model, whether stable or unstable without care of initial conditions. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, Harmbal, has been developed based on the HBM. The method as well as convergence improvements and continuations facilities are thorougly presented and discussed in the present paper. Application of the method is demonstrated on various problems related to a common model of the clarinet: a reed modelled as a simple spring with and without mass and damping, a nonlinear coupling and a cubic simplification of it, and a cylindrical bore with or without dissipation and dispersion as well as a bore formed as a stepped cone.
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"abstract": "The harmonic balance method (HBM) was originally developed for finding\nperiodic solutions of electronical and mechanical systems under a periodic\nforce, but has later been adapted to self-sustained musical instruments. Unlike\ntime-domain methods, this frequency-domain method does not capture transients\nand so is not adapted for sound synthesis. However, its independence of time\nmakes it very useful for studying every periodic solution of the model, whether\nstable or unstable without care of initial conditions. A computer program for\nsolving general problems involving nonlinearly coupled exciter and resonator,\nHarmbal, has been developed based on the HBM. The method as well as convergence\nimprovements and continuations facilities are thorougly presented and discussed\nin the present paper. Application of the method is demonstrated on various\nproblems related to a common model of the clarinet: a reed modelled as a simple\nspring with and without mass and damping, a nonlinear coupling and a cubic\nsimplification of it, and a cylindrical bore with or without dissipation and\ndispersion as well as a bore formed as a stepped cone.",
"arxiv_id": "physics/0503047",
"authors": [
"Snorre Farner",
"Christophe Vergez",
"Jean Kergomard",
"Aude Liz\u00e9e"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1121/1.2166602",
"title": "Contribution to harmonic balance calculations of periodic oscillation for self-sustained musical instruments with focus on single-reed instruments",
"url": "https://arxiv.org/abs/physics/0503047"
},
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