%0 Journal Article
%T Statistical estimation of mechanical parameters of clarinet reeds using experimental and numerical approaches
%+ Conservatoire de musique
%+ Laboratoire Kastler Brossel (LKB (Lhomond))
%+ Laboratoire Charles Coulomb (L2C)
%+ Laboratoire d'Acoustique de l'Université du Mans (LAUM)
%+ Sons
%A Taillard, Pierre-André
%A Laloë, Franck
%A Gross, Michel
%A Dalmont, Jean-Pierre
%A Kergomard, Jean
%< avec comité de lecture
%@ 1610-1928
%J Acta Acustica united with Acustica
%I Hirzel Verlag
%V 100
%N 3
%P 555-573
%8 2014-05-01
%D 2014
%Z 1202.2114
%R 10.3813/AAA.918735
%K Clarinet
%K reed
%K reed instruments
%K acoustics
%K vibration
%Z PACS 43.75
%Z Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]
%Z Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph]
%Z Engineering Sciences [physics]/Acoustics [physics.class-ph]Journal articles
%X 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}.
%G English
%2 https://hal.science/hal-00668277v2/document
%2 https://hal.science/hal-00668277v2/file/taillard_12.pdf
%L hal-00668277
%U https://hal.science/hal-00668277
%~ ENS-PARIS
%~ UPMC
%~ LKB
%~ CNRS
%~ UNIV-AMU
%~ UNIV-LEMANS
%~ LMA_UPR7051
%~ ALLINSP
%~ EC-MARSEILLE
%~ L2C
%~ PSL
%~ UPMC_POLE_2
%~ MIPS
%~ UNIV-MONTPELLIER
%~ LAUM
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ ENS-PSL
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021
%~ PEIRESC