Statistical Parameters under Stationary Random Excitation

Abstract

Fundamental statistical parameters used to describe stationary random vibrations are viewed with emphasis on those parameters of special concern in structural response and failure prediction problems. Included in the review are correlation and spectral density functions, instantaneous and peak value probability density functions, arbitrary level crossing statistics, and elementary considerations in the first passage problem. The relevance of the various statistical parameters to the prediction of structural fatigue and extreme value failures, assuming simple failure mechanism models, is introduced in qualitative terms. Both theoretical and experimental results are displayed to illustrate important relationships. Special attention is given to the importance of underlying assumptions inherent in classical applications, in particular, the excitation normality and system underlying assumptions. Data are presented to demonstrate the impact of common nonlinearities on such response parameters as the instantaneous and peak value probability density functions. Finally, the importance of the stationarity and associated constant parameter system assumptions are discussed from a practical viewpoint. Illustrations are included to clarify the types of errors that result when nonstationary random excitations and responses are analyzed as if they were stationary.