[Bandes interdites et vibrations dans une plaque de Reissner–Mindlin fortement hétérogène]
On étudie lʼinfluence de fortes hétérogénéités sur la propagation des ondes dans une plaque de Reissner–Mindlin. On montre que lorsque certaines caractéristiques élastiques sont comparables à la taille des microstructures du composite il apparaît des bandes interdites, i.e. des intervalles de fréquences – les bandes interdites – pour lesquels la propagation des ondes ne peut pas se faire ou bien est restreinte à certaines polarisations.
We consider an elastic plate governed by the Reissner–Mindlinʼs model, i.e., whose equilibrium equations introduce a coupling between the vertical displacement and the rotation of the normal. This structure is made of a composite with a periodic arrangement of strongly heterogeneous materials and some characteristics of the heterogeneities are comparable to the size of the microstructures. We show that, when the size of the microstructures tends to zero, the limit homogeneous structure presents, for some wavelengths, a negative “mass density” tensor. This means that there exist intervals of frequencies – the band gaps – for which wave propagation is suppressed, or restricted to certain polarizations.
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@article{CRMATH_2011__349_13-14_777_0,
author = {Rohan, Eduard and Miara, Bernadette},
title = {Band gaps and vibration of strongly heterogeneous {Reissner{\textendash}Mindlin} elastic plates},
journal = {Comptes Rendus. Math\'ematique},
pages = {777--781},
publisher = {Elsevier},
volume = {349},
number = {13-14},
year = {2011},
doi = {10.1016/j.crma.2011.05.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.05.013/}
}
TY - JOUR AU - Rohan, Eduard AU - Miara, Bernadette TI - Band gaps and vibration of strongly heterogeneous Reissner–Mindlin elastic plates JO - Comptes Rendus. Mathématique PY - 2011 SP - 777 EP - 781 VL - 349 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.05.013/ DO - 10.1016/j.crma.2011.05.013 LA - en ID - CRMATH_2011__349_13-14_777_0 ER -
%0 Journal Article %A Rohan, Eduard %A Miara, Bernadette %T Band gaps and vibration of strongly heterogeneous Reissner–Mindlin elastic plates %J Comptes Rendus. Mathématique %D 2011 %P 777-781 %V 349 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.05.013/ %R 10.1016/j.crma.2011.05.013 %G en %F CRMATH_2011__349_13-14_777_0
Rohan, Eduard; Miara, Bernadette. Band gaps and vibration of strongly heterogeneous Reissner–Mindlin elastic plates. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 777-781. doi : 10.1016/j.crma.2011.05.013. http://www.numdam.org/articles/10.1016/j.crma.2011.05.013/
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