Overview

Random vibration may be caused by the turbulent flow of gases or liquids, the passage of vehicles over rough surfaces, rough seas acting on ships and marine structures, and earthquakes. The aerospace field also provides many examples of random vibration, and these tend to fall into three groups: flight through atmospheric turbulence, 'separated' airflow over wings and other surfaces and 'mixing noise' from rocket and jet exhaust plumes.

So far, we have looked at the response of systems to deterministic inputs consisting of known functions of time, and there is, potentially at least, an exact answer, provided we have all the data. If the input is a random function of time, and has been recorded, then this approach is still possible, but the calculation would have to be stepwise, very lengthy, and the response would be specific to that particular input. However, if the average properties of the input do not change too much with time, much easier methods can be used. These require the introduction of new ways of describing the average properties of time histories. In this chapter, therefore, we first introduce two new concepts: amplitude probability and the power spectrum. These allow two of the most common tasks in day-to-day work to be tackled: measuring random vibration and calculating the response of linear systems to it. We can then fill in some of the theoretical gaps, introducing correlation functions and their relationship to power spectra and cross-power spectra; some applications of cross-power spectra; and the practical...