Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches
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Authors
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Publication date
2014
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Type
01A - Journal article
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Parent work
Acta Acustica united with Acustica
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DOI of the original publication
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Series
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Volume
100
Issue / Number
Pages / Duration
555-573
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Publisher / Publishing institution
Hirzel
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Abstract
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: EL and GLT . 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 Arundo donax.
Keywords
Musical acoustics
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ISBN
ISSN
0001-7884
1436-7947
1610-1928
1861-9959
1436-7947
1610-1928
1861-9959
Language
English
Created during FHNW affiliation
Yes
Strategic action fields FHNW
Publication status
Published
Review
Peer review of the complete publication
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Citation
Taillard, P.-A., Gross, M., Dalmont, J.-P., Kergomard, J., & Laloë, F. (2014). Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches. Acta Acustica United with Acustica, 100, 555–573. https://doi.org/10.3813/AAA.918735