Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings - INRIA - Institut National de Recherche en Informatique et en Automatique Accéder directement au contenu
Article Dans Une Revue Communications on Pure and Applied Analysis Année : 2012

Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings

Résumé

We consider N Euler-Bernoulli beams and N strings alternatively connected to one another and forming a particular network which is a chain beginning with a string. We study two stabilization problems on the same network and the spectrum of the corresponding conservative system: the characteristic equation as well as its asymptotic behavior are given. We prove that the energy of the solution of the rst dissipative system tends to zero when the time tends to in nity under some irrationality assumptions on the length of the strings and beams. On another hand we prove a polynomial decay result of the energy of the second system, independently of the length of the strings and beams, for all regular initial data. Our technique is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.
Fichier principal
Vignette du fichier
Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings.pdf (231.94 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00644058 , version 1 (28-09-2021)

Identifiants

Citer

Kais Ammari, Denis Mercier, Virginie Régnier, Julie Valein. Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings. Communications on Pure and Applied Analysis, 2012, 11 (2), pp.785--807. ⟨10.3934/cpaa.2012.11.785⟩. ⟨hal-00644058⟩
229 Consultations
49 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More