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

Released on by René Dáger
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  • Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures Book Detail

  • Author : René Dáger
  • Release Date : 2006-08-23
  • Publisher : Springer Science & Business Media
  • Genre : Science
  • Pages : 227
  • ISBN 13 : 3540377263
  • File Size : 74,74 MB
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Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by René Dáger PDF Summary

Book 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.

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Wave Propagation in Structures

Wave Propagation in Structures

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This third edition builds on the introduction of spectral analysis as a means of investigating wave propagation and transient oscillations in structures. Each c