A Finite Element Dynamic Primer
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.
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
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Order Ref: R0017
Editor - D. Hitchings
First Published - January 1992
Hardback, 258 Pages