This book is based on a number of lectures presented at CISM* -Course
on "Stochastic Methods in Structural Mechanics", August 28 -30,1985 in
Udine, Italy. The chapters presented here are either expanded and/or
updated versions of these lectures. The purpose is to introduce readers
to basic principles of stochastic methods of structural mechanics,
particularly to those of dynamics. For those readers who wish to pursue
the study further, the references provided in each chapter will serve as
a useful source of information. Nevertheless the readers find some of
the advanced topics presented by the authors immediately useful for
their own application. The first section of Chapter 1 introduces the
reader to the basic principles of probability theory followed by the
discussion of methods to calculate time invariant structural reliability
estimates, where the exact methods are particularly emphasized. The
Chapter continues with a first introduction to the theory of stochastic
processes. The properties of Gaussian and other type of processes are
discussed. In dealing with observed data, tests of stationarity, as well
as methods to estimate power spectra are described in some detail. The
Chapter closes with a first treatice of excursions of stochastic
processes in terms of number and duration of excursions, extremes,
envelopes and time to first excursions. In Chapter 2 linear structures
under stochastic loading are analyzed by applying the concepts as
outlined in Chapter 1. The analyses are carried out in the time and
frequency range respectively.
