A spectral study of an infinite axisymmetric elastic layer
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 849-863.

Nous présentons ici une étude théorique des modes propres dans une couche élastique axisymétrique. La modélisation mathématique permet de ramener ce problème à l’étude spectrale d’une suite d’opérateurs A n , n∈ℕ, non bornés et autoadjoints dans un espace de Hilbert adéquat. On montre que le spectre essentiel de A n est un intervalle du type [γ,+∞[ et que, sous certaines conditions portant sur les coefficients du milieu, le spectre discret est non vide.

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators A n , n∈ℕ, in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [γ,+∞[ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

Classification : 35P15, 47A70, 73D30
Mots-clés : elasticity, axisymmetry, eigenmodes, min-max principle 
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Chorfi, Lahcène. A spectral study of an infinite axisymmetric elastic layer. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 849-863. http://www.numdam.org/item/M2AN_2001__35_5_849_0/

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