Wave propagation within some non-homogeneous continua

Nirmal Antonio Tamarasselvame (1) , Manuel Buisson (1) , Lalaonirina Rakotomanana-Ravelonarivo (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 Mummer's 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.

Mots clés: Waves; Continuum mechanics; Weakly continuous medium; Non-homogeneous continuum; Wave equation; Stop-pass frequency; Confluent hypergeometric function

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Nirmal Antonio Tamarasselvame, Manuel Buisson, Lalaonirina Rakotomanana-Ravelonarivo. Wave propagation within some non-homogeneous continua. Comptes Rendus Mécanique, 2011, 339 (12), pp.779-788. ⟨10.1016/j.crme.2011.09.002⟩. ⟨hal-00671154⟩