On the modeling of narrow gaps using the standard boundary element method

Vicente Cutanda Henríquez, Peter Møller Juhl, Finn Jacobsen

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Abstract

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers Like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications. (C) 2001 Acoustical Society of America.
Original languageEnglish
JournalJournal of the Acoustical Society of America
Volume109
Issue number4
Pages (from-to)1296-1303
Number of pages8
ISSN0001-4966
Publication statusPublished - 2001

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