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Metamaterials with fibers of elliptic cross section

Abstract : The paper presents the study of elastic composites acting as resonant metamaterials. The composites are made of long bers of elliptic cross section. The condition for obtaining resonant metamaterials is presented in the context of homogenization by using asymptotic expansion. It is shown that inner resonance occurs in the case of soft inclusions embedded within a sti er matrix, both components having mass densities of the same order of magnitude. The localization problem coming from the asymptotic expansion is solved in the case of bers with elliptic cross sections, leading to the dynamic density of the material. The dynamic density is characterized by resonance frequencies and the related eigenfunctions of the inclusions, that are obtained by using an expansion along Mathieu functions. The method allows us to obtain the (orthotropic) dynamic densityrelated to various cases of elliptic cross section, recovering the extreme cases of circular cross-sections and nearly plate inclusions.
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https://hal-upec-upem.archives-ouvertes.fr/hal-02529224
Contributor : Guy Bonnet <>
Submitted on : Thursday, April 2, 2020 - 10:59:11 AM
Last modification on : Friday, April 3, 2020 - 1:47:40 AM

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  • HAL Id : hal-02529224, version 1

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Guy Bonnet, Vincent Monchiet. Metamaterials with fibers of elliptic cross section. Eurodyn2020, National Technical University of Athens, Nov 2020, Athens, Greece. ⟨hal-02529224⟩

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