1st Edition

Random Vibration Mechanical, Structural, and Earthquake Engineering Applications

By Zach Liang, George C. Lee Copyright 2015
    672 Pages 192 B/W Illustrations
    by CRC Press

    Most textbooks on random vibrations are very mathematically intensive, and are often difficult for senior/graduate students to digest in the learning period of a single semester course. This book is designed to focus on basic methodologies to handle random process in engineering practices. Based on our teaching experience, this book can help students to directly gain the necessary knowledge and basic concept of random process, which used to be very difficult through math-intensive logic-rigorous training with conventional textbooks.

    Section I Basic Probability Theory


    Background of Random Vibration

    Fundamental Concept of Probability Theory

    Random Variables

    Functions of Random Variables

    Systems and Functions

    Sums of Random Variables

    Other Functions of Random Variables

    Design Considerations

    Central Limit Theorems and Applications

    Section II Random Process

    Random Processes in the Time Domain

    Definitions and Basic Concepts

    Stationary Process

    Correlation Analysis

    Random Processes in the Frequency Domain

    Spectral Density Function

    Spectral Analysis

    Practical Issues of PSD Functions

    Spectral Presentation of Random Process

    Statistical Properties of Random Process

    Level Crossings


    Accumulative Damages

    Section III Vibrations

    Single-Degree-of-Freedom Vibration Systems

    Concept of Vibration

    Periodically Forced Vibration

    Response of SDOF System to Arbitrary Forces

    Response of SDOF Linear Systems to Random Excitations

    Stationary Excitations

    White Noise Process

    Engineering Examples

    Coherence Analyses

    Time Series Analysis

    Random Vibration of MDOF Linear Systems


    Direct Model for Determining Responses

    Normal Mode Method

    Nonproportionally Damped Systems, Complex Modes

    Modal Combination

    Section IV Applications and Further Discussions

    Inverse Problems

    Introduction to Inverse Problems

    System Parameter Identification

    Vibration Testing

    Failures of Systems

    3σ Criterion

    First Passage Failure


    Considerations on Reliability Design

    Nonlinear Vibrations and Statistical Linearization

    Nonlinear Systems

    Nonlinear Random Vibrations

    Monte Carlo Simulations




    Zach Liang, George C. Lee

    "Random vibration is an important branch in [the] area of dynamic structure. At the same time, it is an obscure portion to most engineering students and researchers. In this book, the author present[s] a clear method to resolve this difficulty, by showing lots of real examples or practical engineering following the basic concept about stochastic process. It constructs a bridge between these two parts instead of basing rigorous mathematical logic creatively."
    —Professor Baitao Sun, Institute of Engineering Mechanics, China Earthquake Administration, Harbin

    "… an excellent resource for students to learn basic methodologies handling random processes and a great reference material for researchers exploring their research on principles of multiple hazard design for structures. … admirable for its content … The authors successfully make a breakthrough that avoids mathematical difficulties for students to absorb the essential concepts needed to account for random data and processes, and effectively help readers apply the methodologies to solve their problems. … exceptional material for the study of random vibration."
    —Kuo-Chun Chang, Professor, Department of Civil ngineering, National Taiwan University, Director, National Center for Research on Earthquake Engineering, Taipei, Taiwan