Now in its second edition, Probabilistic Models for Dynamical Systems expands on the subject of probability theory. Written as an extension to its predecessor, this revised version introduces students to the randomness in variables and time dependent functions, and allows them to solve governing equations.
- Introduces probabilistic modeling and explores applications in a wide range of engineering fields
- Identifies and draws on specialized texts and papers published in the literature
- Develops the theoretical underpinnings and covers approximation methods and numerical methods
- Presents material relevant to students in various engineering disciplines as well as professionals in the field
This book provides a suitable resource for self-study and can be used as an all-inclusive introduction to probability for engineering. It presents basic concepts, presents history and insight, and highlights applied probability in a practical manner. With updated information, this edition includes new sections, problems, applications, and examples. Biographical summaries spotlight relevant historical figures, providing life sketches, their contributions, relevant quotes, and what makes them noteworthy. A new chapter on control and mechatronics, and over 300 illustrations rounds out the coverage.
Table of Contents:
Introduction
Applications
Units
Organization of the Text
Quotes
Problems
Events and Probability
Sets
Probability
Summary
Quotes
Problems
Random Variable Models
Probability Distribution Function
Probability Density Function
Probability Mass Function
Mathematical Expectation
Mean Value
Useful Continuous Probability Density Functions
Discrete Density Functions
Moment-Generating Function
Two Random Variables
Summary
Quotes
Problems
Functions of Random Variables
Exact Functions of One Variable
Functions of Two or More Random Variables
Approximate Analysis
Monte Carlo Methods
Summary
Quotes
Problems
Random Processes
Basic Random Process Descriptors
Ensemble Averaging
Stationarity
Correlations of Derivatives
Fourier Series and Fourier Transforms
Harmonic Processes
Power Spectra
Narrow- and Broad-Band Processes
Interpretations of Correlations and Spectra
Spectrum of Derivative
Fourier Representation of a Stationary Process
Summary
Quotes
Problems
Single Degree-of-Freedom Vibration
Motivating Examples
Newton’s Second Law
Free Vibration With No Damping
Harmonic Forced Vibration With No Damping
Free Vibration with Viscous Damping
Forced Harmonic Vibration
Impulse Excitation
Arbitrary Loading
Frequency Response Function
SDOF: The Response to Random Loads
Response to Two Random Loads
Summary
Quotes
Problems
Multi Degree-of-Freedom Vibration
Deterministic Vibration
Response to Random Loads
Periodic Structures
Inverse Vibration
Random Eigenvalues
Summary
Quotes
Problems
Continuous System Vibration
Deterministic Continuous Systems
The Eigenvalue Problem
Deterministic Vibration
Random Vibration of Continuous Systems
Beams with Complex Loading
Summary
Quotes
Problems
Reliability
Introduction
First Excursion Failure
Other Failure Laws
Fatigue Life Prediction
Summary
Quotes
Problems
Nonlinear and Stochastic Dynamic Models
The Phase Plane
Statistical Equivalent Linearization
Perturbation Methods
The Mathieu Equation
The van der Pol Equation
Markov Process-Based Models
Summary
Quotes
Problems
Non-stationary Models
Envelope Function Model
Non-stationary Generalizations
Priestley’s Model
Oscillator Response
Multi Degree-of-Freedom Oscillator Response
Nonstationary and Nonlinear Oscillator
Summary
Quotes
Problems
Monte Carlo Methods
Introduction
Random Number Generation
Joint Random Numbers
Error Estimates
Applications
Summary
Quotes
Problems
Fluid-Induced Vibration
Ocean Currents and Waves
Fluid Forces in General
Examples
Available Numerical Codes
Summary
Quotes
Probabilistic Models in Controls and Mechatronic Systems
Concepts of Deterministic Systems
Concepts of Stochastic Systems
Filtering of Random Signals
White Noise Filters
Stochastic System Models
The Kalman Filter
Additional Issues
Summary
Quotes
Index
About the Author :
Dr. Haym Benaroya received a B.E. from The Cooper Union for the Advancement of Science and Art, in 1976, and his M.S. and Ph.D. from the University of Pennsylvania, in 1977 and 1981. He worked for Weidlinger Associates, Consulting Engineers, New York, between 1981 and 1989, after which time he joined Rutgers University. He is currently a professor of mechanical and aerospace engineering at Rutgers. Professor Benaroya is an elected member of the International Academy of Astronautics. His research interests include structures and vibration, offshore structural dynamics, fluid-structure interaction, aircraft structures, and the development of concepts for lunar structures. Related interests include science, space and defense policy, and educational methods and policy.
Dr. Seon Mi Han received a B.E. from The Cooper Union for the Advancement of Science and Art in 1996, and her M.S. and Ph.D. from Rutgers, the State University of New Jersey, in 1998 and 2001. She received the Woods Hole Oceanographic Institution Postdoctoral Scholarship between 2001 and 2003. She was an assistant professor of mechanical engineering at Texas Tech University between 2004 and 2010, and is currently an instructor at the university. Her research interests include vibration and dynamics of offshore and marine structures.
Dr. Mark Nagurka received a B.S.E. and M.S.E. in mechanical engineering and applied mechanics from the University of Pennsylvania in 1978 and 1979. He received a Ph.D. in mechanical engineering from M.I.T. in 1983. He taught at Carnegie Mellon University before joining Marquette University, where he is an associate professor of mechanical and biomedical engineering. Professor Nagurka is a Fellow of the American Society of Mechanical Engineers and a licensed professional engineer in Wisconsin and Pennsylvania. His research interests include design of mechanical and electromechanical systems, design of control systems, mechatronics, automation, human-machine interaction, and vehicle dynamics.
