• Accueil   >  
  • Reference   >  
  • Science   >  
  • Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures
Téléchargez le livre : Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures

Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures



de

,

Éditeur :

Springer


Collection :

Mathématiques et Applications

Paru le : 2006-08-23



eBook Téléchargement , DRM LCP 🛈 DRM Adobe 🛈
Lecture en ligne (streaming)
45,35 €
Téléchargement immédiat
Dès validation de votre commande
Ajouter à ma liste d'envies
Image Louise Reader présentation

Louise Reader

Lisez ce titre sur l'application Louise Reader.

badge apple Application Louise Reader
badge Android Application Louise Reader
Description
This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.
Pages
230 pages
Collection
Mathématiques et Applications
Parution
2006-08-23
Marque
Springer
EAN papier
9783540272397
EAN PDF
9783540377269
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
23
Taille du fichier
1761 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
45,35 €

Suggestions personnalisées