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Research Papers

An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

[+] Author and Article Information
Mario Durán1

Facultad de Ingeniería, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chilemduran@ing.puc.cl

Jean-Claude Nédélec

Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, Francenedelec@cmap.polytechnique.fr

Sebastián Ossandón

Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chilesebastian.ossandon@ucv.cl

1

Corresponding author.

J. Vib. Acoust 131(3), 031001 (Apr 07, 2009) (9 pages) doi:10.1115/1.3085894 History: Received May 04, 2005; Revised January 19, 2009; Published April 07, 2009

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Domain of wave propagation

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Figure 2

The lowest eigenfrequencies of the test example (3.4)

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Figure 3

The eigenfrequencies of the test example (3.4) for the case of small wavelengths

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Figure 4

The lowest eigenfrequencies computed by using real Galerkin matrices

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Figure 5

Computed eigenfrequencies for the sphere using matrix A(ω)

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Figure 6

Computed eigenfrequencies for the sphere using matrix AR(ω)

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