Probability Models in Engineering and Science

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    Probability Models in Engineering and Science

    Probability Models in Engineering and Science (Mechanical Engineering (Marcell Dekker)



    Haym Benaroya and Seon Mi Han,
    «Probability Models in Engineering and Science»
    CRC | ISBN 0824723155 | June 24, 2005 | PDF | 10,3 Mb | 760 Pages





    Probabilistic Models in Engineering and Science provides engineers, scientists, and students with a self-contained, comprehensive introduction to applied probabilistic modeling. Perfectly suited to undergraduate and graduate coursework, professional reference, or self-study, this book develops applied probability along with the historical context of the field, providing short biographies and portraits of key \"names\" mentioned in the book. The authors have included extensive example problems, ample end-of-chapter problems, and footnotes that provide references for further in-depth information. Topics include random processes, reliability, and the Monte Carlo method.

    ----


    Certainty exists only in idealized models. Viewed as the quantification of uncertainties, probabilitry 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.

    # Offers an easy-to-follow approach that makes complex concepts accessible and relevant
    # Includes a wealth of example problems, some that work to explain concepts and others that integrate several concepts to show how the theory works as a whole
    # Contains many end-of-chapter exercises that reinforce concepts
    # Devotes a chapter to fluid induced vibration that demonstrates the application of probabilistic models to offshore structural engineering


    :::::::::::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

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