[Sur les équations homogénéisées des oscillations longitudinales du viscoélastoplastique matériau d'Ishlinskii avec données non régulières rapidement oscillantes à deux échelles]
Nous étudions l'homogénéisation du système d'équations décrivant les oscillations longitudinales du matériau viscoélastoplastique d'Ishlinskii, avec des données rapidement oscillantes. La propriété principale est la présence de l'operateur de l'hystérèse de Prandl–Ishlinskii. Nous justifions rigoureusement la convergence vers un problème limite pour un système d'équations operateur-intégro-différentielles homogéneisées à deux échelles, pour lequel nous prouvons un théorème d'existence. Les résultats sont globaux par rapport au temps et aux données.
We study the initial-boundary value problems for a system of operator-differential equations describing Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth coefficients and initial data. The main feature is an presence of hysteresis Prandtl–Ishlinskii operator. We rigorously justify the passage to the corresponding limit initial-boundary value problems for a system of two-scale homogenized operator-integro-differential equations, including the existence theorem for the limit problems. The results are global with respect to the time interval and the data.
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Mot clés : Solides et structures
Andrey Amosov 1 ; Ivan Goshev 1
@article{CRMECA_2006__334_12_713_0,
author = {Andrey Amosov and Ivan Goshev},
title = {On two-scale homogenized equations of the {Ishlinskii} type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth data},
journal = {Comptes Rendus. M\'ecanique},
pages = {713--718},
publisher = {Elsevier},
volume = {334},
number = {12},
year = {2006},
doi = {10.1016/j.crme.2006.10.007},
language = {en},
}
TY - JOUR AU - Andrey Amosov AU - Ivan Goshev TI - On two-scale homogenized equations of the Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth data JO - Comptes Rendus. Mécanique PY - 2006 SP - 713 EP - 718 VL - 334 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2006.10.007 LA - en ID - CRMECA_2006__334_12_713_0 ER -
%0 Journal Article %A Andrey Amosov %A Ivan Goshev %T On two-scale homogenized equations of the Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth data %J Comptes Rendus. Mécanique %D 2006 %P 713-718 %V 334 %N 12 %I Elsevier %R 10.1016/j.crme.2006.10.007 %G en %F CRMECA_2006__334_12_713_0
Andrey Amosov; Ivan Goshev. On two-scale homogenized equations of the Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth data. Comptes Rendus. Mécanique, Volume 334 (2006) no. 12, pp. 713-718. doi : 10.1016/j.crme.2006.10.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.10.007/
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