Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation
A reed instrument model with N acoustical modes can be described as a 2N dimensional autonomous nonlinear dynamical system. Here, a simplified model of a reed-like instrument having two quasi-harmonic resonances, represented by a four dimensional dynamical system, is studied using the continuation a...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2020-01-01
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| Series: | Acta Acustica |
| Online Access: | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2020/06/aacus200016/aacus200016.html |
| _version_ | 1797723739862859776 |
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| author | Gilbert Joel Maugeais Sylvain Vergez Christophe |
| author_facet | Gilbert Joel Maugeais Sylvain Vergez Christophe |
| author_sort | Gilbert Joel |
| collection | DOAJ |
| description | A reed instrument model with N acoustical modes can be described as a 2N dimensional autonomous nonlinear dynamical system. Here, a simplified model of a reed-like instrument having two quasi-harmonic resonances, represented by a four dimensional dynamical system, is studied using the continuation and bifurcation software AUTO. Bifurcation diagrams of equilibria and periodic solutions are explored with respect to the blowing mouth pressure, with focus on amplitude and frequency evolutions along the different solution branches. Equilibria and periodic regimes are connected through Hopf bifurcations, which are found to be direct or inverse depending on the physical parameters values. Emerging periodic regimes mainly supported by either the first acoustic resonance (first register) or the second acoustic resonance (second register) are successfully identified by the model. An additional periodic branch is also found to emerge from the branch of the second register through a period-doubling bifurcation. The evolution of the oscillation frequency along each branch of the periodic regimes is also predicted by the continuation method. Stability along each branch is computed as well. Some of the results are interpreted in terms of the ease of playing of the reed instrument. The effect of the inharmonicity between the first two impedance peaks is observed both when the amplitude of the first is greater than the second, as well as the inverse case. In both cases, the blowing pressure that results in periodic oscillations has a lowest value when the two resonances are harmonic, a theoretical illustration of the Bouasse-Benade prescription. |
| first_indexed | 2024-03-12T10:07:05Z |
| format | Article |
| id | doaj.art-19d8a9ddc7f142eba9e3fd6b628add79 |
| institution | Directory Open Access Journal |
| issn | 2681-4617 |
| language | English |
| last_indexed | 2024-03-12T10:07:05Z |
| publishDate | 2020-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Acta Acustica |
| spelling | doaj.art-19d8a9ddc7f142eba9e3fd6b628add792023-09-02T11:11:07ZengEDP SciencesActa Acustica2681-46172020-01-01462710.1051/aacus/2020026aacus200016Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuationGilbert Joel0Maugeais Sylvain1Vergez Christophe2Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613Laboratoire Manceau de Mathématiques – Le Mans UniversitéAix Marseille Univ, CNRS, Centrale Marseille, LMA, UMR 7031A reed instrument model with N acoustical modes can be described as a 2N dimensional autonomous nonlinear dynamical system. Here, a simplified model of a reed-like instrument having two quasi-harmonic resonances, represented by a four dimensional dynamical system, is studied using the continuation and bifurcation software AUTO. Bifurcation diagrams of equilibria and periodic solutions are explored with respect to the blowing mouth pressure, with focus on amplitude and frequency evolutions along the different solution branches. Equilibria and periodic regimes are connected through Hopf bifurcations, which are found to be direct or inverse depending on the physical parameters values. Emerging periodic regimes mainly supported by either the first acoustic resonance (first register) or the second acoustic resonance (second register) are successfully identified by the model. An additional periodic branch is also found to emerge from the branch of the second register through a period-doubling bifurcation. The evolution of the oscillation frequency along each branch of the periodic regimes is also predicted by the continuation method. Stability along each branch is computed as well. Some of the results are interpreted in terms of the ease of playing of the reed instrument. The effect of the inharmonicity between the first two impedance peaks is observed both when the amplitude of the first is greater than the second, as well as the inverse case. In both cases, the blowing pressure that results in periodic oscillations has a lowest value when the two resonances are harmonic, a theoretical illustration of the Bouasse-Benade prescription.https://acta-acustica.edpsciences.org/articles/aacus/full_html/2020/06/aacus200016/aacus200016.html |
| spellingShingle | Gilbert Joel Maugeais Sylvain Vergez Christophe Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation Acta Acustica |
| title | Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation |
| title_full | Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation |
| title_fullStr | Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation |
| title_full_unstemmed | Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation |
| title_short | Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation |
| title_sort | minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model bouasse benade prescription assessed through numerical continuation |
| url | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2020/06/aacus200016/aacus200016.html |
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