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Probabilistic Methods in the Theory of Structures Strength of Materials Random Vibrations and Random Buckling 3rd Edition by Isaac Elishakoff ISBN 978-9813149854 981314985X

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Probabilistic Methods in the Theory of Structures Strength of Materials Random Vibrations and Random Buckling 3rd Edition Isaac Elishakoff Digital Instant Download

Author(s): Isaac Elishakoff
ISBN(s): 9789813149847, 9813149841
Edition: 3rd
File Details: PDF, 66.30 MB
Year: 2017
Language: english
SKU: EB-6714556 Category: Tag:

Probabilistic Methods in the Theory of Structures Strength of Materials Random Vibrations and Random Buckling 3rd Edition by Isaac Elishakoff  – Ebook PDF Instant Download/Delivery: 978-9813149854, 981314985X
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Product details: 

ISBN 10: 981314985X

ISBN 13: 978-9813149854

Author: Isaac Elishakoff

Exceeds maximum length of 2000 characters; Reviews of the previous edition: “. . . This is a beautiful book . . .” Dr Stephen H Crandall Ford Professor of Engineering, MIT “. . . It is an impressive volume . . .” Prof Warner T Koiter Delft University of Technology, The Netherlands “. . . This extremely well-written text, authored by one of the leaders in the field, incorporates many of these new applications . . . Professor Elishakoff’s techniques for developing the material are accomplished in a way that illustrates his deep insight into the topic as well as his expertise as an educator . . . Clearly, the second half of the text provides the basis for an excellent graduate course in random vibrations and buckling . . . Professor Elishakoff has presented us with outstanding instrument for teaching . . .” Prof Frank Kozin Polytechnic Institute of New York, American Institute of Aeronautics and Astronautics Journal “. . . By far the best book on the market today . . .” Prof Niels C Lind University of Waterloo, Canada “. . . A good book; a different book . . . It is hoped that the success of this book will encourage the author to provide sequel in due course . . .” Prof John D Robson University of Glasgow, England Journal of Sound and Vibration “. . . The book certainly satisfies the need that now exists for a readable textbook and reference book . . .” Prof Masanobu Shinozuka Columbia University “. . . Author ties together reliability, random vibration and random buckling . . . Well written . . . useful book . . .” Dr H Saunders Shock and Vibration Digest “. . . A very useful text that includes a broad spectrum of theory and application is by I Elishakoff” Prof Haim Benaroya Prentice Hall book Mechanical Vibration “. . . A treatise on random vibration and buckling. . .The reviewer wishes to compliment the author for the completion of a difficult task in preparing this book on a subject matter, which is still developing in many fronts . . .” Prof James T P Yao Texas A
 

Table of contents: 

1. Introduction

2. Probability Axioms
2.1. Random Event
2.2. Sample Space
2.3. Probability Axioms
2.4. Equiprobable Events
2.5. Probability and Relative Frequency
2.6. Conditional Probability
2.7. Independent Events
2.8. Reliability of Statically Determinate Truss
2.9. Overall Probability and Bayes’ Formula
Problems

3. Single Random Variable
3.1. Random Variable
3.2. Distribution Function
3.3. Properties of the Distribution Function
3.4. Mathematical Expectation
3.5. Moments of Random Variable; Variance
3.6. Characteristic Function
3.7. Conditional Probability Distribution and Density Functions
3.8. Inequalities of Bienaymé and Tchebycheff
Problems

4. Examples of Probability Distribution and Density Functions. Functions of a Single Random Variable
4.1. Causal Distribution
4.2. Discrete Uniform Distribution
4.3. Binomial or Bernoulli Distribution
4.4. Poisson Distribution
4.5. Rayleigh Distribution
4.6. Exponential Distribution
4.7. Chi-Square (x²) Distribution with m Degrees of Freedom
4.8. Gamma Distribution
4.9. Weibull Distribution
4.10. Normal or Gaussian Distribution
4.11. Truncated Normal Distribution
4.12. Function of a Random Variable
4.13. Moments of a Function of a Random Variable
4.14. Distribution and Density Functions of a Function of a Random Variable (Special Case)
4.15. Linear Function of a Random Variable
4.16. Exponents and Logarithms of a Random Variable
4.17. Distribution and Density Functions of a Function of a Random Variable (General Case)
4.18. Example of Application of the Probabilistic Approach in an Engineering Decision Problem
Problems

5. Reliability of Structures Described by a Single Random Variable
5.1. A Bar under Random Force
5.2. A Bar with Random Strength
5.3. A Bar with a Random Cross-Sectional Area
5.4. A Beam under a Random Distributed Force
5.5. Static Imperfection-Sensitivity of a Nonlinear Model Structure
5.6. Dynamic Imperfection-Sensitivity of a Nonlinear Model Structure
5.7. Axial Impact of a Bar with Random Initial Imperfections
Problems

6. Two or More Random Variables
6.1. Joint Distribution Function of Two Random Variables
6.2. Joint Density Function of Two Random Variables
6.3. Conditional Probability Distribution and Density Functions
6.4. Multidimensional Random Vector
6.5. Functions of Random Variables
6.6. Expected Values, Moments, Covariance
6.7. Approximate Evaluation of Moments of Functions
6.8. Joint Characteristic Function
6.9. Pair of Jointly Normal Random Variables
6.10. Several Jointly Normal Random Variables
6.11. Functions of Random Variables
6.12. Complex Random Variables
Problems

7. Reliability of Structures Described by Several Random Variables
7.1. Fundamental Case
7.2. Bending of Beams under Several Random Concentrated Forces
7.3. Bending of Beams under Several Random Concentrated Moments
7.4. The Central Limit Theorem and Reliability Estimate
Problems

8. Elements of the Theory of Random Functions
8.1. Definition of a Random Function
8.2. First- and Second-Order Distribution Functions
8.3. Moment Functions
8.4. Properties of the Autocovariance Function
8.5. Probability Density Function
8.6. Normal Random Function
8.7. Joint Distribution of Random Functions
8.8. Complex Random Functions
8.9. Stationary Random Functions
8.10. Spectral Density of a Stationary Random Function
8.11. Differentiation of a Random Function
8.12. Integration of a Random Function
8.13. Ergodicity of Random Functions
Problems

9. Random Vibration of Discrete Systems
9.1. Response of a Linear System Subjected to Deterministic Excitation
9.2. Response of a Linear System Subjected to Random Excitation
9.3. Random Vibration of a Multidegree-of-Freedom System
9.4. Illustration of the Role of Modal Cross Correlations
Problems

10. Random Vibration of Continuous Structures
10.1. Random Fields
10.2. Normal Mode Method
10.3. Determination of Joint and Cross Acceptances
10.4. Case Capable of Closed-Form Solution
10.5. Crandall’s Problem
10.6. Random Vibration Due to Boundary-Layer Turbulence
10.7. Analytic Approximations for Pressure Fluctuations in a Turbulent Boundary Layer
10.8. Flutter and Random Vibration of Beams — Approximate Solution
Problems

11. Monte Carlo Method
11.1. Description of the Method
11.2. Generation of Random Numbers
11.3. Simulation of Continuous Random Variables
11.4. Simulation of Random Vectors
11.5. Method of Linear Transformation
11.6. Simulation of Random Functions
11.7. Buckling of a Bar on a Nonlinear Foundation

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Tags: Isaac Elishakoff, Probabilistic Methods, the Theory, Structures Strength