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On the use of Lamb modes in the linear sampling method for elastic waveguides

Laurent Bourgeois 1 Frédérique Le Louër 1 Éric Lunéville 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper is devoted to a modal formulation of the linear sampling method in elastic 2D or 3D waveguide, that is we use the guided modes (called Lamb modes in 2D) as incident waves and the corresponding far fields in order to retrieve some obstacles. We provide the mathematical background to tackle the problem of identifiability and the justification of the linear sampling method for such a case. The elastic waveguide raises a specific issue: it concerns the projection of the scattered field on a transverse basis, which requires the introduction of new variables that mix displacement and stress components and satisfy the so-called Fraser's biorthogonality condition. Some numerical experiments in 2D show the feasibility of the reconstruction in the case of a finite number of incident waves formed by Lamb modes. © 2011 IOP Publishing Ltd.
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Submitted on : Friday, August 30, 2013 - 3:14:38 PM
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Laurent Bourgeois, Frédérique Le Louër, Éric Lunéville. On the use of Lamb modes in the linear sampling method for elastic waveguides. Inverse Problems, 2011, 27 (5), pp.055001. ⟨10.1088/0266-5611/27/5/055001⟩. ⟨hal-00849575⟩



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