Introduction to random vibrations

Many engineering problems concern the vibration of mechanical structures subjected to random forces. Let cite slender structures excited by wind, offshore platforms excited by waves, road-excited vehicles, buildings subjected to earthquakes, aircraft fuselages excited by a turbulent boundary layer, etc.

The objective of this course is to provide elements of random vibrations. We shall introduce the concepts of random signal and its spectral properties and provide methods for estimating the probabilistic response of systems. Many examples will illustrate the concepts and results discussed.

1. Stochastic processes: Generality on probability, random variable, random vector, stochastic process, spectral analysis, continuity, derivation, integration
2. Mechanical vibrations: 1 degree of freedom oscillator, n degrees of freedom systems, deformable solids
3. Spectral response of linear systems: Presentation of the problem, average, correlation and spectrum of the response, correlation and spectrum between excitation and response
4. Probability of threshold and maxima: Probability density of the response, threshold crossing, occurrence of maxima