# Inverse problems in vibration

Book

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

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 109-118
8. G. M. L. Gladwell
Pages 119-140
9. G. M. L. Gladwell
Pages 141-188
10. G. M. L. Gladwell
Pages 189-218
11. G. M. L. Gladwell
Pages 219-256
12. Back Matter
Pages 257-263

### 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

1. 1.Faculty of EngineeringUniversity of WaterlooWaterlooCanada

### Bibliographic information

• Book Title Inverse problems in vibration
• Authors G.M.L. Gladwell
• Series Title Mechanics: Dynamical Systems
• 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
• Hardcover ISBN 978-90-247-3408-5
• Softcover ISBN 978-94-015-1180-3
• eBook ISBN 978-94-015-1178-0
• Series ISSN 0169-667X
• Edition Number 1
• Number of Pages , 284
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

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