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Book review

Author(s) Géradin, M.
Rixen, D.
Title Théorie des vibration (Application à la dynamique des structures)
Publisher Masson
Year of publication 1993
Reviewed by Mihai Postolache

In structural dynamics there exist many situations that involve the knowledge of the vibration theory, for example the finite element method analysis applied for the free vibrations of structures. This book provides an exposition on some important topics from vibration theory such that: analytical dynamics of discrete systems, undamped and damped vibrations, continuous systems and some methods for approximation of continuous systems as well as eigenvalue solution techniques and direct methods for time-integration necessary to solve the structural dynamic equations. The text has been written for a wide range of readers whose work involves the applied vibration theory and computer analysis such that: scientists, structural engineers, physicists, applied mathematicians, undergraduate and postgraduate students.

The book offer a particular extension for Lagrange equations, Hamilton's principle and Rayleigh-Ritz method. The main algorithms covered are the Lanczos and Subspace iteration methods for solving large eigenvalues problems, static and dynamic substructuring (Guyan & Irons) as well as explicit integration methods using central differences. The relationship to finite element method is considered (both truss element and beam element are included as well as their elementary stiffness matrices). In this book can be found numerous examples from structural mechanics and theoretical physics.

Many examples and pictures carefully plotted illustrate the concepts and formulae. Every chapter contains a comprehensive bibliography. The book includes a large number of worked exercises which lead to individual experimental work and independent study. Some algorithms are presented by flow diagrams and for each of them are analyzed the convergence, the consistency, the stability. The book is mathematically rigorous presented, strict proofs are given. A knowledge of the operator theory and numerical analysis is assumed, and an introductory course in mechanics is very advantageous.

There exists a table of index and the table of contents (both in English and French) is sufficiently detailed. The book is very well produced. Covering most of the ideas and techniques required in the third cycle of a structural engineering course, this book also provides an introduction to the mathematics used in more advanced work in the areas of professional practice. Since structural dynamics is also relevant in mechanics, theoretical physics and all I expect that this book will be of interest to workers in these fields and all those who can read french. I strongly recommend it to all scientists seriously wishing to learn about vibration theory and its applications in the structural dynamics.