Hochschule für Musik / Schola Cantorum Basiliensis

Dauerhafte URI für die Sammlunghttps://irf.fhnw.ch/handle/11654/51

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Autor:in: search.filters.author.Laloë, FranckDateien dazu vorhanden?: Nein

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    Publikation
    Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches
    (Hirzel, 2014) Taillard, Pierre-André; Gross, Michel; Dalmont, Jean-Pierre; Kergomard, Jean; Laloë, Franck
    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.
    01A - Beitrag in wissenschaftlicher Zeitschrift
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    Publikation
    Iterated maps for clarinet-like systems
    (Springer, 2010) Taillard, Pierre-André; Kergomard, Jean; Laloë, Franck
    The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.).
    01A - Beitrag in wissenschaftlicher Zeitschrift