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Iterative determination of the sound transmission loss of rectangular thin plates

 
: Aoki, Y.; Maysenhölder, W.

Möser, M. ; Deutsche Gesellschaft für Akustik -DEGA-, Berlin; TU Berlin; Hochschule für Technik, Berlin:
Fortschritte der Akustik. 36. Deutsche Jahrestagung für Akustik 2010. Bd.2 : 15.-18. März 2010, Berlin; DAGA 2010
Berlin: DEGA, 2010
ISBN: 978-3-9808659-8-2
pp.539-540
Deutsche Jahrestagung für Akustik (DAGA) <36, 2010, Berlin>
English
Conference Paper
Fraunhofer IBP ()

Abstract
Iterative schemes and domain decomposition are attractive methods for solving large-scale computational systems. With regard to sound transmission problems it appears as a natural choice to perform separate calculations in each fluid and solid domain and connect them in an iterative manner. However, it is known that a straightforward realization of this procedure may diverge. Several possibilities to overcome this problem are investigated in this paper. Since increase of plate damping reduces the frequency bands with divergent behavior, the introduction of additional damping, which is compensated for somewhere else in the scheme, seems to be a promising strategy. In mathematical terms this physical idea corresponds to the splitting method. The latter can also be used to avoid computationally expensive matrix inversions. The difficulty lies in the optimal choice of the free parameters of the auxiliary matrix. Considerably less parameters, typically one or two, have to be optimized, if relaxation techniques are applied. Such relaxation parameters can even be used for modifications of the physical continuity conditions at the fluid-solid interfaces. If the original conditions are replaced by suitable linear combinations of them, the iteration will converge.

 

Iterative schemes and domain decomposition are attractive methods for solving large-scale computational systems. With regard to sound transmission problems it appears as a natural choice to perform separate calculations in each fluid and solid domain and connect them in an iterative manner. However, it is known that a straightforward realization of this procedure may diverge. Several possibilities to overcome this problem are investigated in this paper. Since increase of plate damping reduces the frequency bands with divergent behavior, the introduction of additional damping, which is compensated for somewhere else in the scheme, seems to be a promising strategy. In mathematical terms this physical idea corresponds to the splitting method. The latter can also be used to avoid computationally expensive matrix inversions. The difficulty lies in the optimal choice of the free parameters of the auxiliary matrix. Considerably less parameters, typically one or two, have to be optimized, if relaxation techniques are applied. Such relaxation parameters can even be used for modifications of the physical continuity conditions at the fluid-solid interfaces. If the original conditions are replaced by suitable linear combinations of them, the iteration will converge.

: http://publica.fraunhofer.de/documents/N-143661.html