394 articles – 1385 references  [version française]
 HAL: hal-00668277, version 1
 arXiv: 1202.2114
 Measurements of resonance frequencies of clarinet reeds and simulations
 (2012-02-09)
 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}.
 1: Conservatoire de musique Conservatoire de musique 2: Laboratoire Kastler Brossel (LKB (Lhomond)) CNRS : UMR8552 – Université Pierre et Marie Curie [UPMC] - Paris VI – Ecole normale supérieure de Paris - ENS Paris 3: Laboratoire Charles Coulomb (L2C) CNRS : UMR5221 – Université Montpellier II - Sciences et techniques 4: Laboratoire d'acoustique de l'université du Maine (LAUM) CNRS : UMR6613 – Université du Maine 5: Laboratoire de Mécanique et d'Acoustique (LMA) CNRS : UPR7051
 Subject : Physics/Physics/General PhysicsPhysics/Mechanics/AcousticsEngineering Sciences/Acoustics
 Keyword(s): Clarinet – reed – reed instruments – acoustics – vibration
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 hal-00668277, version 1 http://hal.archives-ouvertes.fr/hal-00668277 oai:hal.archives-ouvertes.fr:hal-00668277 From: Jean Kergomard <> Submitted on: Thursday, 9 February 2012 14:55:24 Updated on: Monday, 5 November 2012 18:14:59