1st Edition
Random Vibration Mechanical, Structural, and Earthquake Engineering Applications
Section I Basic Probability Theory
IntroductionBackground 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
