Wave Propagation, Observation and Control in 1 - D Flexible Multi-Structures
Format: Paperback
ISBN13: 9783540272397
Paperback|9783540272397
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Overview
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.
| ISBN-13 | 9783540272397 |
|---|---|
| ISBN-10 | 3540272399 |
| Weight | 0.76 Pounds |
| Dimensions | 6.10 x 0.55 x 9.25 In |
| List Price | $69.95 |
| Edition | 1st Edition |
| Format | Paperback |
|---|---|
| Language | English |
| Pages | x, 230 pages |
| Publisher | Springer |
| Published On | 2005-09-02 |
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