Introduction to Random Vibrations

Introduction to Random Vibrations presents a brief review of probability theory, a concise treatment of random variables and random processes, and a comprehensive exposition of the theory of random vibrations.

This is the first comprehensive text on its subject to appear since the 1960s. It incorporates classical material with the many significant developments in the field and is the only up-to-date introduction currently available. Introduction to Random Vibrations presents a brief review of probability theory, a concise treatment of random variables and random processes (including normal, Poisson, and Markov processes), and a comprehensive exposition of the theory of random vibrations. It contains a number of noteworthy features. Linear systems theory is introduced with a high degree of generality in order to demonstrate its elegance and range of applicability. The response of discrete and continuous linear systems to random excitations is then developed within this framework. The chapter on the response of nonlinear systems represents a unified view of the topic, incorporating some major recent formulations. The discrete-state approach, which has emerged as a powerful technique, is utilized in the treatment of a number of random process properties, among them level crossings, peaks, envelopes, and first-passage times. The Stieltje integral representation of random processes is introduced in order to simplify the presentation of stationary and nonstationary random processes and response statistics. In addition to the opening review of probability and set theory, appendices review relevant topics in Fourier analysis and ordinary differential equations. Both these reviews and exercises included with the chapters will be useful to students using the book as a course text and to practitioners using it as a reference.

This book is third in The MIT Press Series in Structural Mechanics, edited by Max Irvine.