Probabilistic models for dynamical systems / Haym Benaroya, Seon Mi Han and Mark Nagurka.

Includes index.

1. Introduction
1.1 Applications
1.2 Units
1.3 Organization of the Text
1.4 Quotes
1.5 Problems
2. Events and Probability
2.1 Sets
2.2 Probability
2.3 Summary
2.4 Quotes
2.5 Problems
3. Random Variable Models
3.1 Probability Distribution Function
3.2 Probability Density Function
3.3 Probability Mass Function
3.4 Mathematical Expectation
3.4.1 Mean Value
3.4.2 Variance
3.5 Useful Continuous Probability Density Functions
3.6 Discrete Density Functions
3.7 Moment-Generating Function
3.8 Two Random Variables
3.9 Summary
3.10 Quotes
3.11 Problems
4. Functions of Random Variables
4.1 Exact Functions of One Variable
4.2 Functions of Two or More Random Variables
4.3 Approximate Analysis
4.4 Monte Carlo Methods
4.5 Summary
4.6 Quotes
4.7 Problems
5. Random Processes
5.1 Basic Random Process Descriptors
5.2 Ensemble Averaging
5.3 Stationarity
5.4 Correlations of Derivatives
5.5 Fourier Series and Fourier Transforms
5.6 Harmonic Processes
5.7 Power Spectra
5.8 Narrow- and Broad-Band Processes
5.9 Interpretations of Correlations and Spectra
5.10 Spectrum of Derivative
5.11 Fourier Representation of a Stationary Process
5.12 Summary
5.13 Quotes
5.14 Problems
6. Single Degree-of-Freedom Vibration
6.1 Motivating Examples
6.2 Newton's Second Law
6.3 Free Vibration With No Damping
6.4 Harmonic Forced Vibration With No Damping
6.5 Free Vibration with Viscous Damping
6.6 Forced Harmonic Vibration
6.7 Impulse Excitation
6.8 Arbitrary Loading
6.9 Frequency Response Function
6.10 SDOF: The Response to Random Loads
6.11 Response to Two Random Loads
6.12 Summary
6.13 Quotes
6.14 Problems
7. Multi Degree-of-Freedom Vibration
7.1 Deterministic Vibration
7.2 Response to Random Loads
7.3 Periodic Structures
7.4 Inverse Vibration
7.5 Random Eigenvalues
7.6 Summary
7.7 Quotes
7.8 Problems
8. Continuous System Vibration
8.1 Deterministic Continuous Systems
8.1 The Eigenvalue Problem
8.3 Deterministic Vibration
8.4 Random Vibration of Continuous Systems
8.5 Beams with Complex Loading
8.6 Summary
8.7 Quotes
8.8 Problems
9. Reliability
9.1 Introduction
9.2 First Excursion Failure
9.3 Other Failure Laws
9.4 Fatigue Life Prediction
9.5 Summary
9.6 Quotes
9.7 Problems
10. Nonlinear and Stochastic Dynamic Models
10.1 The Phase Plane
10.2 Statistical Equivalent Linearization
10.3 Perturbation Methods
10.4 The Mathieu Equation
10.5 The van der Pol Equation
10.6 Markov Process-Based Models
10.7 Summary
10.8 Quotes
10.9 Problems
11. Nonstationary Models
11.1 Envelope Function Model
11.2 Nonstationary Generalizations
11.3 Priestley's Model
11.4 Oscillator Response
11.5 Multi Degree-of-Freedom Oscillator Response
11.6 Nonstationary and Nonlinear Oscillator
11.7 Summary
11.8 Quotes
11.9 Problems
12. Monte Carlo Methods
12.1 Introduction
12.2 Random Number Generation
12.3 Joint Random Numbers
12.4 Error Estimates
12.5 Applications
12.6 Summary
12.7 Quotes
12.8 Problems
13. Fluid-Induced Vibration
13.1 Ocean Currents and Waves
13.2 Fluid Forces in General
13.3 Examples
13.4 Available Numerical Codes
13.5 Summary
13.6 Quotes
14. Probabilistic Models in Controls and Mechatronic Systems 14.1 Concepts of Deterministic Systems
14.2 Concepts of Stochastic Systems
14.3 Filtering of Random Signals
14.4 White Noise Filters
14.5 Stochastic System Models
14.6 The Kalman Filter
14.7 Additional Issues
14.8 Summary
14.9 Quotes
Index

This book includes biographical summaries of relevant historical figures, providing life sketches, major contributions and relevant quotes from their works.