Certainty exists only in idealized models. Viewed as the quantification of uncertainties, probability and random processes play a significant role in modern engineering, particularly in areas such as structural dynamics. Unlike this book, however, few texts develop applied probability in the practical manner appropriate for engineers. "Probability Models in Engineering and Science" provides a comprehensive, self-contained introduction to applied probabilistic modeling. The first four chapters present basic concepts in probability and random variables, and while doing so, develop methods for static problems. The remaining chapters address dynamic problems, where time is a critical parameter in the randomness.Highlights of the presentation include numerous examples and illustrations and an engaging, human connection to the subject, achieved through short biographies of some of the key people in the field. End-of-chapter problems help solidify understanding and footnotes to the literature expand the discussions and introduce relevant journals and texts.
This book builds the background today's engineers need to deal explicitly with the scatter observed in experimental data and with intricate dynamic behavior. Designed for undergraduate and graduate coursework as well as self-study, the text's coverage of theory, approximation methods, and numerical methods make it equally valuable to practitioners.
Table of Contents
INTRODUCTION Applications Units Organization of the Text Problems EVENTS AND PROBABILITY Sets Probability Concluding Summary Problems RANDOM VARIABLE MODELS Probability Distribution Function Probability Density Function Mathematical Expectation Variance USEFUL PROBABILITY DENSITIES Two Random Variables Concluding Summary Problems FUNCTIONS OF RANDOM VARIABLES Exact Functions of One Variable Functions of Two or More RVs General Case Approximate Analysis Monte Carlo Method Concluding Summary Problems The Standard Normal Table RANDOM PROCESSES Basic Random Process Descriptors Ensemble Averaging Stationarity Derivatives of Stationary Processes Fourier Series and Fourier Transforms Harmonic Processes Power Spectra Fourier Representation of a Random Process Borgman's Method of Frequency Discretization Concluding Summary Problems SINGLE DEGREE OF FREEDOM DYNAMICS Motivating Examples Deterministic SDoF Vibration SDoF: The Response to Random Loads Response to Two Random Loads Concluding Summary Problems MULTI DEGREE OF FREEDOM VIBRATION Deterministic Vibration Response to Random Loads Periodic Structures Inverse Vibration Random Eigenvalues Concluding Summary Problems CONTINUOUS SYSTEM VIBRATION Deterministic Continuous Systems Sturm-Liouville Eigenvalue Problem Deterministic Vibration Random Vibration of Continuous System Beams with Complex Loading Concluding Summary Problems RELIABILITY Introduction First Excursion Failure Fatigue Life Prediction Concluding Summary Problems NONLINEAR DYNAMIC MODELS Examples of Nonlinear Vibration Fundamental Nonlinear Equations Statistical Equivalent Linearization Perturbation Methods The van der Pol Equation Markov Process Based Models Concluding Summary Problems NONSTATIONARY MODELS Some Applications Envelope Function Model Nonstationary Generalizations Priestley's Model SDoF Oscillator Response Multi DoF Oscillator Response Nonstationary and Nonlinear Oscillator Concluding Summary Problems THE MONTE CARLO METHOD Introduction Random Number Generation Joint Random Numbers Error Estimates Applications Concluding Summary Problems FLUID INDUCED VIBRATION Ocean Currents and Waves Fluid Forces - In General Examples Available Numerical Codes Index