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A spectral study of an infinite axisymmetric elastic layer

Published online by Cambridge University Press:  15 April 2002

Lahcène Chorfi
Lahcène Chorfi*
Affiliation:
Département de Mathématiques, Université Badji Mokhtar de Annaba, BP 12, 23000 Annaba, Algeria.
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Abstract

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, $n\in \mathbb{N}$, in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type $[\gamma,+\infty[$ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

Keywords

Elasticityaxisymmetryeigenmodesmin-max principle.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001 , pp. 849 - 863
Copyright
© EDP Sciences, SMAI, 2001

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