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Inverse problems in vibration

  • G. M. L. Gladwell

Part of the Mechanics: Dynamical Systems book series (MDYS, volume 9)

Table of contents

  1. Front Matter
    Pages N1-x
  2. G. M. L. Gladwell
    Pages 1-17
  3. G. M. L. Gladwell
    Pages 19-43
  4. G. M. L. Gladwell
    Pages 45-58
  5. G. M. L. Gladwell
    Pages 59-75
  6. G. M. L. Gladwell
    Pages 77-107
  7. G. M. L. Gladwell
    Pages 119-140
  8. G. M. L. Gladwell
    Pages 141-188
  9. G. M. L. Gladwell
    Pages 189-218
  10. G. M. L. Gladwell
    Pages 219-256
  11. Back Matter
    Pages 257-263

About this book

Introduction

The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theory is the determination of the natural frequencies (eigen­ frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen­ functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec­ tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties.

Keywords

inverse problem vibration

Authors and affiliations

  • G. M. L. Gladwell
    • 1
  1. 1.Faculty of EngineeringUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-1178-0
  • Copyright Information Springer Science+Business Media B.V. 1986
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-015-1180-3
  • Online ISBN 978-94-015-1178-0
  • Series Print ISSN 0169-667X
  • Buy this book on publisher's site
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