Mathematical analysis of elastic surface waves in topographic waveguides.

Anne-Sophie Bonnet-Ben Dhia 1 Jean Duterte 2 Patrick Joly 2
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
2 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : We present here a theoretical study of the guided waves in an isotropic homogeneous elastic half-space whose free surface has been deformed. The deformation is supposed to be invariant in the propagation direction and localized in the transverse ones. We show that finding guided waves amounts to solving a family of 2-D eigenvalue problems set in the cross-section of the propagation medium. Then using the min-max principle for non-compact self-adjoint operators, we prove the existence of guided waves for some particular geometries of the free surface. These waves have a smaller speed than that of the Rayleigh wave in the perfect half-space and a finite transverse energy. Moreover, we prove that the existence results are valid for arbitrary high frequencies in the presence of singularities of the free boundary. Finally, we prove that no guided mode can exist at low frequency, except maybe the fundamental one.
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Journal articles
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01010335
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Submitted on : Thursday, June 19, 2014 - 3:34:14 PM
Last modification on : Thursday, July 4, 2019 - 4:00:50 AM

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Anne-Sophie Bonnet-Ben Dhia, Jean Duterte, Patrick Joly. Mathematical analysis of elastic surface waves in topographic waveguides.. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 1999, 9 (5), pp.755-798. ⟨10.1142/S0218202599000373⟩. ⟨hal-01010335⟩

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