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# A Finite Element Dynamic Primer

**This book is intended to address the problems that a practising
finite element analyst might encounter when carrying out a
vibration analysis. It is not intended to be a text book on
dynamics, of which there are many excellent examples suggested in
the bibliography. The contents are more concerned with giving
practical help and advice to an analyst, both before he starts the
analysis and in isolating possible problems that might occur as the
analyst is being conducted. This makes the layout of the text
rather different from other books on dynamics. It can be considered
to consist of two sections, the first being chapter 1 and the
second section being the rest of the book. Chapter 1 consists of
brief notes and comments in terms of guidelines for a dynamic
analysis. This can be used to remind the analyst of possible
pitfalls associated with any analysis. However, dynamics are more
complicated than statics and there are many more variations of the
problem and solution types. All of these possible combinations
means that it is impossible to give a complete list of guidelines
and so the second section of the book, from chapter 2 onwards,
expands the brief notes given in chapter 1. These are intended to
explain to the analyst the underlying theory associated with the
brief notes so that he can adapt and interpret the comments to suit
his own special problem.**

No mathematics is given in chapter 1 but some has to be given in the subsequent chapters to explain the problems under discussion. The mathematics is not complete and is intended to be sufficient for the purposes of explanation. More detailed development of the mathematics associated with a dynamic analysis can be found in dynamics text-books. The contents of each chapter is orientated to the finite element analysis rather than development of vibration theory. As explained above, chapter 1 contains the general guidelines. One of the problems with carrying out any dynamic analysis is the wide variety of problem types and solution types and the plethora of possible solution methods that this can give rise to. Chapter 2 presents details of the solution methods and the types of problem that each is most suited to solving. Chapters 3 and 4 give modelling suggestions, chapter 3 being concerned with general dynamic modelling and chapter 4 with aspects more specific to the finite element method.

Forms of problem reduction, associated with trying to minimise the cost of the analysis are discussed in chapter 5. Since dynamics are less well understood and more difficult to solve than statics there is often a parallel dynamic test program conducted where aspects of the dynamic problem are confirmed by experiment. Chapter 6 discusses some problems of matching test and theory. The basic parameters of a dynamic analysis, the structural stiffness and mass and the applied loadings are usually well defined. However, practical vibrations also have a degree of damping associated with them. The nature of this is imprecise and the assumptions and approximations are detailed in chapter 7. The considerations associated with controlling and understanding the output are presented in chapter 8. One important point to consider here is the shear volume of data that a dynamic analysis can generate. Chapter 9 presents some information of the rather specialised topics of random vibrations and seismic analysis.

The book is not intended to be read from cover to cover. It is anticipated that only sections, not even complete chapters, will be read, as required by the problem in hand. With this in mind, and with the form of the organisation of the text associated with discussing possible problems and providing hints and tips, there is a repetition of some information. An attempt has been made to minimise this but the attitude adopted was that it is better to repeat some comments and warnings if this prevents mistakes from being made, rather than having too many cross-references, which might not be followed.

## Contents

Chapter 1 – BASIC CONSIDERATIONS FOR A DYNAMIC ANALYSIS

Chapter 2 – DYNAMIC PROBLEM TYPES

Chapter 3 – MODELLING

Chapter 4 – FINITE ELEMENT MODELLING

Chapter 5 – PROBLEM REDUCTION

Chapter 6 – DYNAMIC TESTING

Chapter 7 – DAMPING

Chapter 8 – RESULTS INTERPRETATION AND PRESENTATION

Chapter 9 – RANDOM VIBRATIONS AND SEISMIC ANALYSIS

GLOSSARY OF TERMS IN DYNAMIC ANALYSIS

BIBLIOGRAPHY

## Purchasing Details

Members Price__£32__ | $42 | €37

Non-Members Price

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Order Ref: R0017

About

Editor - D. Hitchings

First Published - January 1992

Hardback, 258 Pages