# Probabilistic Models for Dynamical Systems, Second Edition

764 pages | 329 B/W Illus.

Hardback: 9781439849897
pub: 2013-05-01
US Dollars\$125.95
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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.

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

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

Frequency Response Function

SDOF: The Response to Random Loads

Summary

Quotes

Problems

Multi Degree-of-Freedom Vibration

Deterministic Vibration

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

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

Summary

Quotes

Index

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.