APPROXIMATION BIDIMENSIONNELLE DU SPECTRE DE L'OPERATEUR DE POINCARE-STEKLOV ASSOCIE AUX PLAQUES MINCES

Consider the Poincare-Steklov operator associated with the system of linearized three-dimensional elasticity and with the interface Γ 0 e =γ 0 ×]−e,e[ separating the two parts of a single plate of thickness 2e. If the Lame constants vary as e −3 , the spectrum of this operator converges, when e tends to zero, towards the union of the spectrum of the Poincare-Steklov operator associated with γ 0 and with the plate operator in Kirchhoff-Love theory, and of fthe spectrum of the Poincare-Steklov operator associated with γ 0 and with the membrane operator. On considere l'operateur de Pincare-Steklov associe au systeme de l'elasticite tridimensionnelle linearisee et a l'interface Γ 0 e =γ 0 ×]−e, e[ separant deux parties d'une meme plaque d'epaisseur 2e. Si les coefficients de Lame du materiau varient comme e −3 , le spectre de cet operateur converge, lorsque e tend vers zero, vers la reunion du spectre de l'operateur de Pincare-Steklov associe a γ 0 et a l'operateur des plaques en theorie de Kirchhoff-Love, et de celui de l'operateur de Poincare-Steklov associe a γ 0 et a l'operateur de deformation membranaire