Skip to Main content Skip to Navigation
Journal articles

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Fabien Treyssede 1 Khac-Long Nguyen 1 Anne-Sophie Bonnet-Ben Dhia 2 Christophe Hazard 2
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an open waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.
Mots-clés : ONDE
Document type :
Journal articles
Complete list of metadatas

Cited literature [48 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01064430
Contributor : Ifsttar Cadic <>
Submitted on : Tuesday, September 16, 2014 - 12:28:58 PM
Last modification on : Friday, July 17, 2020 - 5:08:52 PM
Long-term archiving on: : Wednesday, December 17, 2014 - 10:51:30 AM

File

doc00019289.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Fabien Treyssede, Khac-Long Nguyen, Anne-Sophie Bonnet-Ben Dhia, Christophe Hazard. Finite element computation of trapped and leaky elastic waves in open stratified waveguides. Wave Motion, Elsevier, 2014, 51 (7), pp.1093-1107. ⟨10.1016/j.wavemoti.2014.05.003⟩. ⟨hal-01064430⟩

Share

Metrics

Record views

570

Files downloads

600