INTRODUCTION

This chapter presents statistical methods for analyzing vibrating systems. Two situations often occur in which a statistical analysis is useful. The first occurs when the excitation of a system appears to be random in time, in which case it is convenient to describe the temporal response of the system statistically rather than deterministically. This form of analysis is called random vibration analysis ^[1] and is presented in the first half of this chapter. The second situation occurs when a system is complicated enough that its resonant modes appear to be distributed randomly in frequency, in which case it is convenient to describe the frequency response of the system statistically rather than deterministically. This form of analysis ^[2] is called statistical energy analysis (SEA) and is presented in the second half of this chapter.

In either situation the randomness need only appear to be so. For example, in random vibration it may be that the excitation could be calculated exactly if enough information were known. However, if the excitation is adequately described by statistical parameters (such as the mean value and variance), then a statistical analysis of the system response is valid. Similarly, in a complicated system the modes can presumably be analyzed deterministically. However, if the modal distribution is adequately described by statistical parameters, then a statistical energy analysis of the system response is valid whether or not the excitation is random.