| Issue |
ESAIM: M2AN
Volume 35, Number 5, September-October 2001
|
|
|---|---|---|
| Page(s) | 849 - 863 | |
| DOI | https://doi.org/10.1051/m2an:2001138 | |
| Published online | 15 April 2002 | |
A spectral study of an infinite axisymmetric elastic layer
Département de Mathématiques, Université Badji Mokhtar de Annaba, BP 12, 23000 Annaba, Algeria.
Received:
23
October
2000
Revised:
5
May
2001
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 An, 
, in a
suitable
Hilbert space. We show that the essential spectrum of An is an interval
of
type 
and that, under certain conditions on the
coefficients
of the medium, the discrete spectrum is non empty.
Résumé
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 An, , non
bornés
et autoadjoints dans un espace de Hilbert adéquat. On montre que le
spectre
essentiel de An est un intervalle du type et que,
sous
certaines conditions portant sur les coefficients du milieu, le spectre
discret
est non vide.
Mathematics Subject Classification: 35P15 / 47A70 / 73D30
Key words: Elasticity / axisymmetry / eigenmodes / min-max principle.
© EDP Sciences, SMAI, 2001
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