A spectral study of an infinite axisymmetric elastic layer
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 849-863

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, 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.

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, 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.

Classification:  35P15,  47A70,  73D30
Keywords: elasticity, axisymmetry, eigenmodes, min-max principle
@article{M2AN_2001__35_5_849_0,
     author = {Chorfi, Lahc\`ene},
     title = {A spectral study of an infinite axisymmetric elastic layer},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {849-863},
     zbl = {0994.35100},
     mrnumber = {1866270},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_5_849_0}
}
Chorfi, Lahcène. A spectral study of an infinite axisymmetric elastic layer. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 849-863. http://www.numdam.org/item/M2AN_2001__35_5_849_0/

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