TABLE OF CONTENTS Although we've learned a lot in the preceding pages, it should also be clear that many problems are still beyond our analytical abilities. Anything that is more complex than a group of lumped spring-mass systems or a simple continuous system, such as a string, is currently beyond our skills. The simple addition of a nonuniform mass to a bar or a spatially varying stiffness in a beam makes the problem too difficult for closed-form analysis. These are the problems that we now address. Our solutions will not be exact, but merely approximate. Luckily, since we'll be able to create these approximate solutions to whatever degree of accuracy we desire, they'll meet all our needs. With the techniques to be introduced in the following pages, you'll be able to analyze quite general systems efficiently and accurately.
This section is probably the shortest in the book. The main focus of this chapter is on so-called modal approximations, i.e., methods that presume the existence of distributed modes for a structure. In the opposite view, one would pay no attention to whether distributed modes might exist but instead would break the problem into little chunks. The finite element method is a well-known approach that takes this second point of view. In this approach the actual continuous body is broken into simpler units (elements) for which displacement/stress relations can be easily calculated. These elements are then joined together in a mesh to approximate the original system. The technique is very...
