Inverse problems in vibration

1. Front Matter

   Pages N1-x

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2. Matrix Analysis

   • G. M. L. Gladwell

   Pages 1-17

3. Vibrations of Discrete Systems

   • G. M. L. Gladwell

   Pages 19-43

4. Jacobian Matrices

   • G. M. L. Gladwell

   Pages 45-58

5. Inversion of Discrete Second-Order Systems

   • G. M. L. Gladwell

   Pages 59-75

6. Further Properties of Matrices

   • G. M. L. Gladwell

   Pages 77-107

7. Some Applications of the Theory of Oscillatory Matrices

   • G. M. L. Gladwell

   Pages 109-118

8. The Inverse Problem for the Discrete Vibrating Beam

   • G. M. L. Gladwell

   Pages 119-140

9. Green’s Functions and Integral Equations

   • G. M. L. Gladwell

   Pages 141-188

10. Inversion of Continuous Second-Order Systems

    • G. M. L. Gladwell

    Pages 189-218

11. The Euler-Bernoulli Beam

    • G. M. L. Gladwell

    Pages 219-256

12. Back Matter

    Pages 257-263

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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.

• inverse problem
• vibration

`This book is a necessary addition to the library of engineers and mathematicians working in vibration theory.'
Mathematical Reviews

• Faculty of Engineering, University of Waterloo, Waterloo, Canada

  G. M. L. Gladwell

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