Comptes Rendus
Wave propagation within some non-homogeneous continua
Comptes Rendus. Mécanique, Volume 339 (2011) no. 12, pp. 779-788.

We investigate the elastic wave propagation within a non-homogeneous continuum according to W. Noll. After some preliminaries in geometry approach suggested by E. Cartan, the linear momentum equation of so-called weakly continuous medium is written. A first example illustrates the modal analysis of an axisymmetric non-homogeneous thick tube. The overall solution is the product of an attenuating exponential response with Kummerʼs functions. The second example deals with a Timoshenko beam involving transversal displacement and angular rotation of section. We observe the presence of various waves with spatial attenuation, either for the displacement or the section rotation, together with the occurring waves at different scale levels.

Nous nous intéressons à la propagation dʼonde élastique à travers un milieu continu non homogène au sens de W. Noll. Après quelques préliminaires sur lʼapproche géométrique suggérée par E. Cartan, la loi de la quantité de mouvement pour un milieu dit faiblement continu est écrite. Un premier exemple illustre lʼanalyse modale dʼun cylindre, à paroi épaisse, non homogène et axisymétrique. Les solutions analytiques sont sous la forme dʼun produit dʼune atténuation exponentielle avec des fonctions de Kummer. Un deuxième exemple étudie une poutre de Timoshenko avec un mouvement transversal et rotatif dʼune section. Nous observons la présence dʼondes différentes avec atténuation spatiale, que ce soit pour le déplacement ou la rotation de la section, ainsi que celles se produisant à différents niveaux dʼéchelle.

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DOI: 10.1016/j.crme.2011.09.002
Keywords: Waves, Continuum mechanics, Weakly continuous medium, Non-homogeneous continuum, Wave equation, Stop-pass frequency, Confluent hypergeometric function
Mot clés : Ondes, Milieux continus, Milieu faiblement continu, Milieu non homogène, Équation des ondes, Fréquence de coupure, Confluent hypergéometrique

Nirmal Antonio Tamarasselvame 1; Manuel Buisson 1; Lalaonirina R. Rakotomanana 1

1 Université européenne de Bretagne, IRMAR – université de Rennes 1, campus Beaulieu, 35042 Rennes cedex, France
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Nirmal Antonio Tamarasselvame; Manuel Buisson; Lalaonirina R. Rakotomanana. Wave propagation within some non-homogeneous continua. Comptes Rendus. Mécanique, Volume 339 (2011) no. 12, pp. 779-788. doi : 10.1016/j.crme.2011.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.09.002/

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