Stochastic Analysis of Linear Systems

Abstract

The stochastic analysis of structural vibrations deals with the description and characterization of structural loads and responses that are modeled as stochastic processes. The probabilistic charac- terization of the input process could be extremely complex in time domain where the probability density functions depend on the autocorrelation functions which experimentally have to be specified over given set points. Since this approach is difficult to be used in applications, stochastic vibration analysis of structural linear systems subjected to Gaussian input processes is quite often performed in the frequency domain by means of the spectral analysis. This analysis is a very powerful tool for the analytical and experimental treatment of a large class of physical as well as structural problems subjected to random excitations. The main reasons are (a) the spectrum has an immediate physical interpretation as a power-frequency distribution; (b) the spectrum provides information on the stochastic structure of the process; and (c) the spectrum may be estimated by fairly simple numerical techniques