Spectre des réseaux de poutresThe eigenvalue problem for networks of beams

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Résumé

Nous analysons le spectre d'un modèle de réseaux de poutres d'Euler-Bernoulli. Nous donnons tout d'abord l'équation caractéristique du spectre. Dans certains cas particuliers, nous montrons que le spectre dépend seulement de la structure du graphe. Finalement, nous donnons le comportement asymptotique des valeurs propres en établissant la formule de Weyl.

Abstract

We consider the spectral analysis of a model of networks of Euler-Bernoulli beams. We first give the characteristic equation for the spectrum. Secondly, in some particular situations, we show that the spectrum depends only on the structure of the graph. Thirdly, we investigate the asymptotic behaviour of the eigenvalues by proving the so-called Weyl's formula.

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