Wave propagation within some non-homogeneous continua |
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Authors: | Nirmal Antonio Tamarasselvame Manuel Buisson |
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Affiliation: | Université européenne de Bretagne, IRMAR - université de Rennes 1, campus Beaulieu, 35042 Rennes cedex, France |
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Abstract: | 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 Kummer?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. |
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Keywords: | Waves Continuum mechanics Weakly continuous medium Non-homogeneous continuum Wave equation Stop-pass frequency Confluent hypergeometric function |
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