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Impedance boundary conditions for acoustic waves in a duct with a step discontinuity
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
2003 (English)Report (Other academic)
Place, publisher, year, edition, pages
2003.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2003-032
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-80167OAI: oai:DiVA.org:uu-80167DiVA: diva2:108081
Available from: 2007-02-07 Created: 2007-02-07 Last updated: 2011-11-17Bibliographically approved
In thesis
1. Numerical Techniques for Acoustic Modelling and Design of Brass Wind Instruments
Open this publication in new window or tab >>Numerical Techniques for Acoustic Modelling and Design of Brass Wind Instruments
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Acoustic horns are used in musical instruments and loudspeakers in order to provide an impedance match between an acoustic source and the surrounding air. The aim of this study is to develop numerical tools for the analysis and optimisation of such horns, with respect to their input impedance spectra. Important effects such as visco-thermal damping and modal conversion are shown to be localised to different parts of a typical brass instrument. This makes it possible to construct hybrid methods that apply different numerical techniques in different parts of the instrument. Narrow and slowly flaring parts are modelled using a one-dimensional transmission line analogy, and the rapidly flaring bell is modelled using a two-dimensional finite-difference method. The connection between the different regions is done by the aid of impedance boundary conditions. The use of such boundary conditions is investigated with respect to the required number of degrees of freedom.

Numerical shape optimisation is employed in order to design horns with desired impedance characteristics throughout a design frequency band. A loudspeaker horn is optimised with respect to its sound power output, and a brass instrument is optimised with respect to its intonation. The horns are modelled using the finite-element method and a transmission line analogy. In order to achieve rapid convergence of the optimisation, gradient based minimisation algorithms are used. A prerequisite for success is the ability to accurately and inexpensively compute the gradient of the objective function. The gradient for the finite-element method is computed by an adjoint equation technique, whereas for the transmission line analogy, it is derived by formal differentiation of the model. In order to find smooth solutions, a smoothing technique is used, where optimisation is done with respect to the right hand side of a Poisson type equation.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2003. 25 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 862
Keyword
Acoustic horn, brass wind instrument, loudspeaker, optimization, hybrid method
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-3507 (URN)91-554-5679-0 (ISBN)
Public defence
2003-09-19, Room 1211, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2003-06-05 Created: 2003-06-05 Last updated: 2011-10-26Bibliographically approved

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