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A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi — 2001

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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 , n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

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