Random Vibrations

by Lutes; Sarkani

• ISBN13: 9780750677653
• ISBN10: 0750677651
• Format: Hardcover
• Copyright: 2003-12-02
• Publisher: Elsevier Science

Summary

The topic of Introduction to Random Vibrations is the behavior of structural and mechanical systems when they are subjected to unpredictable, or random, vibrations. These vibrations may arise from natural phenomena such as earthquakes or wind, or from human-controlled causes such as the stresses placed on aircraft at takeoff and landing. Study and mastery of this topic enables engineers to design and maintain structures capable of withstanding random vibrations, thereby protecting human life. Introduction to Random Vibrations will lead readers in a user-friendly fashion to a thorough understanding of vibrations of linear and nonlinear systems that undergo stochasticrandomexcitation.

Table of Contents

Preface	xi
Chapter 1 Introduction
1.1 Why Study Random Vibration	1	(2)
1.2 Probabilistic Modeling and Terminology	3	(4)
1.3 Approach to the study of Failure Probability	7	(1)
Exercises	8	(3)
Chapter 2 Fundamentals of Probability and Random Variables
2.1 Use of Probability and Random Variable Theory	11	(1)
2.2 Fundamental Concepts of Probability Theory	12	(3)
2.3 Random Variables and Probability Distributions	15	(5)
2.4 Probability Density Functions	20	(6)
2.5 Joint and Marginal Distributions	26	(9)
2.6 Distribution of a Function of a Random Variable	35	(3)
2.7 Conditional Probability Distributions	38	(10)
2.8 Independence of Random Variables	48	(5)
Exercises	53	(6)
Chapter 3 Expected Values of Random Variables
3.1 Concept of Expected Values	59	(1)
3.2 Definition of Expected Values	59	(5)
3.3 Moments of Random Variables	64	(14)
3.4 Conditional Expectation	78	(3)
3.5 Generalized Conditional Expectation	81	(3)
3.6 Characteristic Function of a Random Variable	84	(6)
3.7 Power Series for Characteristic Function	90	(5)
3.8 Importance of Moment Analysis	95	(1)
Exercises	95	(8)
Chapter 4 Analysis of Stochastic Processes
4.1 Concept of a Stochastic Process	103	(2)
4.2 Probability Distribution	105	(2)
4.3 Moment and Covariance Functions	107	(7)
4.4 Stationarity of Stochastic Processes	114	(6)
4.5 Properties of Autocorrelation and Autocovariance	120	(7)
4.6 Limits of Stochastic Processes	127	(5)
4.7 Ergodicity of a Stochastic Process	132	(6)
4.8 Stochastic Derivative	138	(10)
4.9 Stochastic Integral	148	(6)
4.10 Gaussian Stochastic Processes	154	(7)
Exercises
Chapter 5 Time Domain Linear Vibration Analysis
5.1 Deterministic Dynamics	161	(9)
5.2 Evaluation of Impulse Response Functions	170	(7)
5.3 Stochastic Dynamics	177	(4)
5.4 Response to Stationary Excitation	181	(5)
5.5 Delta-Correlated Excitations	186	(7)
5.6 Response of Linear Single-Degree-of-Freedom Oscillator	193	(12)
5.7 Stationary SDF Response to Delta-Correlated Excitation	205	(5)
5.8 Nearly Delta-Correlated Processes	210	(1)
5.9 Response to Gaussian Excitation	211	(1)
Exercises	212	(7)
Chapter 6 Frequency Domain Analysis
6.1 Frequency Content of a Stochastic Process	219	(2)
6.2 Spectral Density Functions for Stationary Processes	221	(5)
6.3 Properties of Spectral Density Functions	226	(2)
6.4 Narrowband Processes	228	(4)
6.5 Broadband Processes and White Noise	232	(2)
6.6 Linear Dynamics and Harmonic Transfer Functions	234	(7)
6.7 Evolutionary Spectral Density	241	(4)
6.8 Response of Linear SDF Oscillator	245	(6)
6.9 Calculating Autospectral Density from a Sample Time History	251	(3)
6.10 Higher-Order Spectral Density Functions	254	(3)
Exercises	257	(4)
Chapter 7 Frequency, Bandwidth, and Ampitude
7.1 General Concepts	261	(1)
7.2 Characteristic Frequency and Bandwidth from Rate of Occurrence	261	(11)
7.3 Frequency Domain Analysis	272	(10)
7.4 Amplitude and Phase of a Stationary Stochastic Process	282	(16)
7.5 Amplitude of a Modulated Stochastic Process	298	(3)
Exercises	301	(6)
Chapter 8 Matrix Analysis of Linear Systems
8.1 Generalization of Scalar Formulation	307	(4)
8.2 Multi-Degree of Freedom Systems	311	(2)
8.3 Uncoupled Modes of MDF Systems	313	(6)
8.4 Time Domain Stochastic Analysis of Uncoupled MDF Systems	319	(9)
8.5 Frequency Domain Analysis of MDF Systems	328	(6)
8.6 State Space Formulation of Equations of Motion	334	(11)
Exercises	345	(6)
Chapter 9 Direct Stochastic Analysis of Linear Systems
9.1 Basic Concept	351	(3)
9.2 Derivation of State-Space Moment and Cumulant Equations	354	(2)
9.3 Equations for First and Second Moments and Covariance	356	(5)
9.4 Simplifications for Delta-Correlated Excitation	361	(4)
9.5 Solution of the State-Space Equations	365	(10)
9.6 Energy Balance and Covariance	375	(6)
9.7 Higher Moments and Cumulants Using Kronecker Notation	381	(10)
9.8 State-Space Equations for Stationary Autocovariance	391	(4)
9.9 Fokker-Planck Equation	395	(16)
Exercises	411	(4)
Chapter 10 Introduction to Nonlinear Stochastic Vibration
10.1 Approaches to the Problem	415	(3)
10.2 Fokker-Planck Equation for Nonlinear System	418	(13)
10.3 Statistical Lmearization	431	(3)
10.4 Linearization of Dynamics Problems	434	(13)
10.5 Linearization of Hysteretic Systems	447	(18)
10.6 State-Space Moment and Cumulant Equations	465	(15)
Exercises	480	(7)
Chapter 11 Failure Analysis
11.1 Modes of Failure	487	(1)
11.2 Probability Distribution of Peaks	488	(7)
11.3 Extreme Value Distribution and Poisson Approximation	495	(9)
11.4 Improved Estimates of the Extreme Value Distribution	504	(10)
11.5 Inclusion-Exclusion Series for Extreme Value Distribution	514	(2)
11.6 Extreme Value of Gaussian Response of SDF Oscillator	516	(4)
11.7 Accumulated Damage	520	(3)
11.8 Stochastic Analysis of Fatigue	523	(6)
11.9 Rayleigh Fatigue Approximation	529	(4)
11.10 Other Spectral Fatigue Methods for Gaussian Stress	533	(10)
11.11 Non-Gaussian Fatigue Effects	543	(7)
Exercises	550	(7)
Chapter 12 Effect of Parameter Uncertainty
12.1 Basic Concept	557	(4)
12.2 Modeling Parameter Uncertainty	561	(1)
12.3 Direct Perturbation Method	562	(4)
12.4 Logarithmic Perturbation Method	566	(3)
12.5 Stationary Response Variance for Delta-Correlated Excitation	569	(9)
12.6 Nonstationary Response Variance for Delta-Correlated Excitation	578	(4)
12.7 Stationary Response Variance for General Stochastic Excitation	582	(8)
12.8 First-Passage Failure Probability	590	(6)
12.9 Fatigue Life	596	(5)
12.10 Multi-Degree-of-Freedom Systems	601	(5)
Exercises	606	(7)
Appendix A Dirac Delta Function	613	(4)
Appendix B Fourier Analysis	617	(6)
References	623	(10)
Author Index	633	(2)
Subject Index	635