Random vibrations focuses on the dynamic response of structural systems under uncertain, time-varying loading. The uncertainty associated with both loading and response is characterized using probabilistic tools. The study of random vibrations is of paramount importance for assessing the level of safety of a dynamic system and studying specific phenomena such as fatigue life.
This lecture provides basic tools for understanding the behavior of systems subject to stochastic actions. The first part of the course focuses on the definition and characterization of random variables and stochastic processes. Special attention is devoted to the analysis of stochastic process in both time and frequency domains. Fundamental properties of random processes such as correlation and spectral density are discussed in depth. The second part of this course focuses on the response of single- and multiple-degree-of-freedom linear systems subject to random processes. The starting point is the analysis and characterization of the response of linear dynamical systems subject to deterministic forces. Then, uncertainty in the forces is considered by means of random processes in order to study the mean, autocorrelation and spectral density of the response of the linear system. The third and final part of the course focuses on some practical applications of random vibrations, with focus on the first-passage failure and fatigue analysis.
Upon successful completion of this course, students will be able to analyze a random process and characterize it in terms of its autocorrelation function and power spectral density function. Moreover, students will be able to analyze and quantify the uncertainty of the response of a linear system subject to an external action characterized as a random process.
The course examination consists of (1) a presentation of the project work and (2) an oral defense of the project results in which the student's knowledge of the course content is evaluated.