Introduction to Operational Modal Analysis

Content: Cover
 Title Page
 Copyright
 Contents
 Preface
 Chapter 1 Introduction
 1.1 Why Conduct Vibration Test of Structures?
 1.2 Techniques Available for Vibration Testing of Structures
 1.3 Forced Vibration Testing Methods
 1.4 Vibration Testing of Civil Engineering Structures
 1.5 Parameter Estimation Techniques
 1.6 Brief History of OMA
 1.7 Modal Parameter Estimation Techniques
 1.8 Perceived Limitations of OMA
 1.9 Operating Deflection Shapes
 1.10 Practical Considerations of OMA
 1.11 About the Book Structure
 References
 Chapter 2 Random Variables and Signals
 2.1 Probability. 2.1.1 Density Function and Expectation2.1.2 Estimation by Time Averaging
 2.1.3 Joint Distributions
 2.2 Correlation
 2.2.1 Concept of Correlation
 2.2.2 Autocorrelation
 2.2.3 Cross Correlation
 2.2.4 Properties of Correlation Functions
 2.3 The Gaussian Distribution
 2.3.1 Density Function
 2.3.2 The Central Limit Theorem
 2.3.3 Conditional Mean and Correlation
 References
 Chapter 3 Matrices and Regression
 3.1 Vector and Matrix Notation
 3.2 Vector and Matrix Algebra
 3.2.1 Vectors and Inner Products
 3.2.2 Matrices and Outer Products
 3.2.3 Eigenvalue Decomposition. 3.2.4 Singular Value Decomposition3.2.5 Block Matrices
 3.2.6 Scalar Matrix Measures
 3.2.7 Vector and Matrix Calculus
 3.3 Least Squares Regression
 3.3.1 Linear Least Squares
 3.3.2 Bias, Weighting and Covariance
 References
 Chapter 4 Transforms
 4.1 Continuous Time Fourier Transforms
 4.1.1 Real Fourier Series
 4.1.2 Complex Fourier Series
 4.1.3 The Fourier Integral
 4.2 Discrete Time Fourier Transforms
 4.2.1 Discrete Time Representation
 4.2.2 The Sampling Theorem
 4.3 The Laplace Transform
 4.3.1 The Laplace Transform as a generalization of the Fourier Transform. 4.3.2 Laplace Transform Properties4.3.3 Some Laplace Transforms
 4.4 The Z-Transform
 4.4.1 The Z-Transform as a generalization of the Fourier Series
 4.4.2 Z-Transform Properties
 4.4.3 Some Z-Transforms
 4.4.4 Difference Equations and Transfer Function
 4.4.5 Poles and Zeros
 References
 Chapter 5 Classical Dynamics
 5.1 Single Degree of Freedom System
 5.1.1 Basic Equation
 5.1.2 Free Decays
 5.1.3 Impulse Response Function
 5.1.4 Transfer Function
 5.1.5 Frequency Response Function
 5.2 Multiple Degree of Freedom Systems
 5.2.1 Free Responses for Undamped Systems. 5.2.2 Free Responses for Proportional Damping5.2.3 General Solutions for Proportional Damping
 5.2.4 Transfer Function and FRF Matrix for Proportional Damping
 5.2.5 General Damping
 5.3 Special Topics
 5.3.1 Structural Modification Theory
 5.3.2 Sensitivity Equations
 5.3.3 Closely Spaced Modes
 5.3.4 Model Reduction (SEREP)
 5.3.5 Discrete Time Representations
 5.3.6 Simulation of OMA Responses
 References
 Chapter 6 Random Vibrations
 6.1 General Inputs
 6.1.1 Linear Systems
 6.1.2 Spectral Density
 6.1.3 SISO Fundamental Theorem
 6.1.4 MIMO Fundamental Theorem
 6.2 White Noise Inputs.