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Ye Lu 2011-03-14

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Stefan Bilbao, 2009, Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics

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F. Avanzini and M. van Walstijn, “Modeling the mechanical response of the reed- mouthpiece-lip system of a clarinet. 1. A one-dimensional distributed model”, Acta Acust, 90, 537-547 (2004).

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Single degree of freedom with constant parameters can only be assumed for oscillations at small amplitudes Reed beating is usually incorporated in a non-physical way by imposing a maximum allowed displacement for the reed tip The dependence of the reed-mouthpiece system on the lip embouchure is not considered in lumped model

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A bar with non-uniform cross-sectional area Clamped to the mouthpiece at one end Additional constraints provided by the mouthpiece profile and interaction with the lip

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One-dimensional: assume no torsional modes in the reed No attempt to model the air flow in the reed channel or to simulate the acoustical resonator

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Finite Difference Method

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Unconditional stable when Θ > 1/4

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http://www.tandfonline.com/doi/abs/10.1080/10236190802385298#preview

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The reed tip can not exceed a certain value The tip is not stopped suddenly but rather gradually

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Thank You!

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