TABLE OF CONTENTS Traditionally, structures have been analysed either as continuous or as discretized ('lumped') systems. Some structures, such as uniform beams, can still usefully be treated as continuous systems, but most are now regarded as discrete multi-DOF systems. The finite element method, in fact, can be said to combine both approaches: it is continuous within the elements, but discrete at the global coordinate level.
In this chapter, discussion of continuous systems has been limited to uniform beams, and the classical Rayleigh-Ritz method. A description of the latter has been included, even though it is now obsolete, to show the historical link with later methods, such as component mode synthesis, the branch mode method and the finite element method, which are still known as 'Rayleigh-Ritz' methods.
Structures tend to be characterized by low damping, justifying the use of real eigenvalues and eigenvectors in most cases, and this will be assumed in this chapter.
The basic principles outlined in Chapter 6, such as the use of energy methods and normal coordinates, are timeless concepts. However, the application of these fundamental principles to everyday tasks in structural dynamics has changed considerably over the years, due to the development of modern computers. Therefore, to put current methods of analysis into perspective, a brief discussion of their historical development is first presented.
To place the various methods for dealing with the vibration of structures in context, it is helpful to consider how they have developed. It will be...
