Exponential stability of a network of serially connected Euler–Bernoulli beams - Archive ouverte HAL Access content directly
Journal Articles International Journal of Control Year : 2014

Exponential stability of a network of serially connected Euler–Bernoulli beams

(1) , (1)
1

Abstract

The aim is to prove the exponential stability of a system modelling the vibrations of a network of N Euler–Bernoulli beams serially connected. Using a result given by K. Ammari and M. Tucsnak, the problem is reduced to the estimate of a transfer function and the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that one of the sufficient conditions for both the estimate of the transfer function and the observability inequality is that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value. This property called spectral gap holds. It is proved using the exterior matrix method due to W. H. Paulsen. Two more asymptotic estimates involving the eigenfunctions are required. They are established using an adequate basis.
Fichier principal
Vignette du fichier
Exponential stability of a network of serially connected.pdf (469.97 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03163679 , version 1 (28-09-2021)

Identifiers

Cite

Denis Mercier, Virginie Régnier. Exponential stability of a network of serially connected Euler–Bernoulli beams. International Journal of Control, 2014, 87 (6), pp.1266-1281. ⟨10.1080/00207179.2013.874597⟩. ⟨hal-03163679⟩
47 View
30 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More