Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methods

Khac-Long Nguyen 1 Fabien Treyssede 1 Christophe Hazard 2
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Résumé : Among the numerous techniques of non destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes become necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.
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Journal of Sound and Vibration, 2015, 344, pp.158-178. <10.1016/j.jsv.2014.12.032>
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Khac-Long Nguyen, Fabien Treyssede, Christophe Hazard. Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methods. Journal of Sound and Vibration, 2015, 344, pp.158-178. <10.1016/j.jsv.2014.12.032>. <hal-01346096v2>

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