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

668 Pages
by CRC Press

Also available as eBook on:

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

Introduction

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

Extrema

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

Modeling

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

Fatigue

Considerations on Reliability Design

Nonlinear Vibrations and Statistical Linearization

Nonlinear Systems

Nonlinear Random Vibrations

Monte Carlo Simulations

References

Index

### Biography

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