TABLE OF CONTENTS Up to this point we've been concerning ourselves with deterministic vibrations, i.e., periodically excited systems. The nice thing about periodic forcings is that once you know one period of the input, you know them all. Nothing else can happen the input is completely determined. Thus we call the excitation deterministic. Although we could continue to restrict ourselves in this way, it turns out that expanding the scope of our excitations to include random vibrations will be very beneficial. For one thing, many systems are subjected to some form of random loading. The wind loads on an airliner, the forces acting on an offshore oil rig, and the accelerations felt by an object in a delivery truck are all well described by a random signal, not a periodically varying one. Furthermore, many of the algorithms used by modal analyzers to determine a system's natural frequencies and mode shapes are based on a random vibrations viewpoint. This chapter presents some of the important information you will need if you ever plan to carry out modal analyses, but please remember that it is just an introduction. The field of random vibrations is quite large, and there is a great deal of material that we won't be considering. Those interested in studying random vibration and modal analysis in more depth can consult other texts [3,9].
We'll start the chapter by laying out some fundamentals of random vibrations and finish by introducing some of the concepts of modal analysis.
Let's begin...
