Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches

Autor: Jean Kergomard, Jean-Pierre Dalmont, Pierre-André Taillard, Michel Gross, Franck Laloë
Přispěvatelé: Conservatoire de musique, Laboratoire Kastler Brossel (LKB (Lhomond)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Acoustique de l'Université du Mans (LAUM), Le Mans Université (UM)-Centre National de la Recherche Scientifique (CNRS), Sons, Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2014
Předmět:
Zdroj: Acta Acustica united with Acustica
Acta Acustica united with Acustica, 2014, 100 (3), pp.555-573. ⟨10.3813/AAA.918735⟩
Acta Acustica united with Acustica, Hirzel Verlag, 2014, 100 (3), pp.555-573. ⟨10.3813/AAA.918735⟩
ISSN: 1610-1928
1861-9959
DOI: 10.3813/aaa.918735
Popis: International audience; A set of 55 clarinet reeds is observed by holography, collecting 2 series of measurements made under 2 different moisture contents, from which the resonance frequencies of the 15 first modes are deduced. A statistical analysis of the results reveals good correlations, but also significant differences between both series. Within a given series, flexural modes are not strongly correlated. A Principal Component Analysis (PCA) shows that the measurements of each series can be described with 3 factors capturing more than $90\%$ of the variance: the first is linked with transverse modes, the second with flexural modes of high order and the third with the first flexural mode. A forth factor is necessary to take into account the individual sensitivity to moisture content. Numerical 3D simulations are conducted by Finite Element Method, based on a given reed shape and an orthotropic model. A sensitivity analysis revels that, besides the density, the theoretical frequencies depend mainly on 2 parameters: $E_L$ and $G_{LT}$. An approximate analytical formula is proposed to calculate the resonance frequencies as a function of these 2 parameters. The discrepancy between the observed frequencies and those calculated with the analytical formula suggests that the elastic moduli of the measured reeds are frequency dependent. A viscoelastic model is then developed, whose parameters are computed as a linear combination from 4 orthogonal components, using a standard least squares fitting procedure and leading to an objective characterization of the material properties of the cane \textit{Arundo donax}.
Databáze: OpenAIRE
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