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Le Développement en Série de Peano du Matricant Pour l'Etude de la Propagation des Ondes Elastiques en Milieux à Propriétés Continûment Variables

Abstract : Modelling elastic media with material properties continuously varying in the lateral direction, has a long historical record in geophysics. The mantle crust, the oceans and the atmosphere are media with natural heterogeneity. Moreover, the continuous variation of the elastic properties often occurs in industrial materials. Characterization of such materials is of great importance.
The classical scheme to solve the wave equation in media with one-dimensional heterogeneity relies on a multilayered model. The properties are piecewise constant functions for both naturally media and the discretization model of continuously varying media. This approach is known as Thomson-Haskell method. For continuously heterogeneous media, this method, via discretization, deals with an approximate problem, thus raising some questions about the accuracy and the validity of the obtained solutions.
In this work, the point is to tackle the problem of wave propagation in heterogeneous media in a different way. To keep the authenticity of the problem, we employ the method based on Peano series expansion of the matricant. For an arbitrary heterogeneity profile, the Peano series expansion of the wave equation written as a first-order ordinary differential system with variable coefficients. The analytical and numerical treatment of the Peano series of the matricant provides a robust method for analysing acoustic phenomena in plates and waveguides. It is hoped to be useful in variousareas dealing with ultrasonic characterization of heterogeneous media.
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https://tel.archives-ouvertes.fr/tel-00113951
Contributor : Cécile Baron <>
Submitted on : Wednesday, November 15, 2006 - 9:34:55 AM
Last modification on : Wednesday, November 29, 2017 - 2:56:43 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 7:36:21 PM

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  • HAL Id : tel-00113951, version 1

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Cécile Baron. Le Développement en Série de Peano du Matricant Pour l'Etude de la Propagation des Ondes Elastiques en Milieux à Propriétés Continûment Variables. Acoustique [physics.class-ph]. Université Sciences et Technologies - Bordeaux I, 2005. Français. ⟨tel-00113951⟩

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