Random Vibrations

Theory and Applications

Yingguang Wang

• Publisher: CRC Press
• Year: 2025
• eBook ISBN: 9781040273548
• Edition: 0
• Topic: Technology & Engineering
• Index: Technology & Engineering

Random Vibrations: Theory and Applications investigates methods and theories involved in random vibration analyses of linear and nonlinear systems, as well as in predicting random vibration induced failures.

This book is a lucid and well-paced introduction to random vibrations, superbly motivated and illustrated through a wealth of convincing applications in various engineering fields. The strong points of the book are its coverage of weakly stationary and ergodic random processes, spectral analysis of random processes, mode displacement superposition method, equivalent linearization technique for nonlinear random vibrations and an updated definition of rain flow cycle for fatigue analysis. Particularly appealing features of the book are its numerous examples and end-of-chapter exercises. This book offers a clear guide to the formulations and mathematical properties of random vibration analysis techniques, with an emphasis on practical applications rather than mathematical development for its own sake. However, some important mathematical formulas have been explicitly deduced in a detailed manner so that readers can go through the material in this book very smoothly and efficiently.

This book is intended for upper undergraduate and graduate students who are interested in learning advanced techniques for performing random vibration analysis, researchers and scientists investigating linear and nonlinear systems under random external excitations, and aeronautical/civil/mechanical/structural/ocean engineers involved in the design and manufacture of real-world stochastically excited engineering systems.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Author
• Chapter 1 Introduction
• Chapter 2 Random Variables and Related Probability Theory
• Chapter 3 Random Processes
• Chapter 4 Spectral Analysis of Random Processes
• Chapter 5 Random Vibration of Single-Degree-of-Freedom Linear Systems
• Chapter 6 Random Vibration of Two-Degree-of-Freedom Linear Systems
• Chapter 7 Random Vibration of Multi-Degree-of-Freedom Linear Systems
• Chapter 8 Random Vibration of Nonlinear Systems
• Chapter 9 Simulation Methods for Random Vibration Analysis
• Chapter 10 Random Vibration Induced Failures
• Appendix A: Derivation of the Parseval Theorem
• Appendix B: Derivation of the Wiener–Khintchine Theorem
• Appendix C: Damping
• Appendix D: Residue Integration in Random Vibrational Analysis
• Appendix E: Theory of Springs
• Bibliography
• Index