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La théorie variationnelle des rayons complexes version Fourier : application aux problèmes tridimensionnels de vibro-acoustique

Abstract : The Variational Theory of Complex Rays (VTCR) is a wave-based computational approach dedicated to the resolution of medium-frequency problems. It uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it verifies the governing equation. Thus, the solution can be approximated using plane waves, which is very interesting in the medium-frequency vibration domain and also leads to a strong convergence of the method. In the previous works, this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands. In this thesis, we propose a new approximation of these amplitudes based on Fourier series. The extension to 3D problems is straightforward thanks to the use of spherical harmonics. We show that this approach increases the robustness of the method as it handles problems of industrial complexity, makes it more efficient numerically thanks to analytical integration and extends its applicability to somewhat higher frequencies.
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https://tel.archives-ouvertes.fr/tel-00624377
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Submitted on : Friday, September 16, 2011 - 4:51:32 PM
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  • HAL Id : tel-00624377, version 1

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Louis Kovalevsky. La théorie variationnelle des rayons complexes version Fourier : application aux problèmes tridimensionnels de vibro-acoustique. Autre. École normale supérieure de Cachan - ENS Cachan, 2011. Français. ⟨NNT : 2011DENS0020⟩. ⟨tel-00624377⟩

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