We extend to the thermoelastic case the study [1] devoted to the dynamic response of a structure made of two linearly elastic bodies linked by a thin soft adhesive linearly elastic layer. Once again, a formulation in terms of an evolution equation in a Hilbert space of possible states with finite energy makes it possible to identify the asymptotic behavior, when some geometrical and thermomechanical parameters tend to their natural limits, as the response of two bodies linked by a thermomechanical constraint. The genuine thermomechanical coupling remains in the constraint law only for a specific relative behavior of the parameters.
On étend au cas thermoélastique l'étude [1] consacrée à la réponse dynamique d'un assemblage de deux corps linéairement élastiques liés par une couche adhésive linéairement élastique mince et molle. À nouveau, une formulation en terme d'équations d'évolution dans un espace de Hilbert d'états possibles d'énergie finie permet d'identifier le comportement asymptotique, lorsque des paramètres géométriques et thermomécaniques tendent vers leurs limites naturelles, comme la réponse de l'assemblage des deux corps par une liaison thermomécanique. Le couplage thermomécanique initial perdure dans la loi de la liaison uniquement pour un comportement relatif particulier des paramètres.
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Mot clés : Problèmes de collage, Thermoélasticité linéarisée, Dynamique, Équations d'évolution, Opérateurs m-dissipatifs
Christian Licht 1, 2, 3; Ahmed Ould Khaoua 4; Thibaut Weller 1
@article{CRMECA_2015__343_1_18_0,
author = {Christian Licht and Ahmed Ould Khaoua and Thibaut Weller},
title = {Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity},
journal = {Comptes Rendus. M\'ecanique},
pages = {18--26},
publisher = {Elsevier},
volume = {343},
number = {1},
year = {2015},
doi = {10.1016/j.crme.2014.09.005},
language = {en},
}
TY - JOUR AU - Christian Licht AU - Ahmed Ould Khaoua AU - Thibaut Weller TI - Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity JO - Comptes Rendus. Mécanique PY - 2015 SP - 18 EP - 26 VL - 343 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2014.09.005 LA - en ID - CRMECA_2015__343_1_18_0 ER -
%0 Journal Article %A Christian Licht %A Ahmed Ould Khaoua %A Thibaut Weller %T Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity %J Comptes Rendus. Mécanique %D 2015 %P 18-26 %V 343 %N 1 %I Elsevier %R 10.1016/j.crme.2014.09.005 %G en %F CRMECA_2015__343_1_18_0
Christian Licht; Ahmed Ould Khaoua; Thibaut Weller. Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity. Comptes Rendus. Mécanique, Volume 343 (2015) no. 1, pp. 18-26. doi : 10.1016/j.crme.2014.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.09.005/
[1] Dynamics of elastic bodies connected by a thin adhesive layer (A. Léger; M. Deschamps, eds.), Ultrasonic Wave Propagation in Non Homogeneous Media, Springer Proc. Phys., vol. 128, Springer, Heidelberg, Germany, 2009
[2] Dynamics of elastic bodies connected by a thin soft viscoelastic layer, J. Math. Pures Appl., Volume 99 (2013) no. 6, pp. 685-703
[3] Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011
[4] Approximation of semi-groups of operators, Pacific J. Math., Volume 28 (1958), pp. 897-919
[5] Dynamics of elastic bodies connected by a thin soft inelastic layer, C. R. Mecanique, Volume 341 (2013), pp. 323-332
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