Linearization Methods for Stochastic Dynamic Systems Book

Introduction     1
References     5
Mathematical Preliminaries     7
Moments and Cumulants of Random Variables     7
Gaussian and Non-Gaussian Distributions     9
Moments and Cumulants of Stochastic Processes     11
Second-Order Stochastic Processes     13
Gaussian and Non-Gaussian Processes     20
Markov Processes     23
Diffusion Processes and Kolmogorov Equations     25
Wiener Process     27
White and Colored Noise     29
Integration and Differentiation Formulas of Diffusion Processes     31
Stochastic Differential Equations     35
Stochastic Stability     43
The Method of Fokker-Planck-Kolmogorov Equations     48
Bibliography Notes     55
References     56
Moment Equations for Linear Stochastic Dynamic Systems (LSDS)     59
Gaussian White Noise External Excitation     60
Gaussian White Noise External and Parametric Excitation     61
Gaussian Colored Noise External and Parametric Excitation     63
Nonstationary Gaussian External Excitation     65
Spectral Method     69
Non-Gaussian External Excitation     74
Bibliography Notes     79
References     80
Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS)     85
Moment Equations for Polynomial SDS Under Parametric and External Gaussian Excitation     86
Simple Closure Techniques     94
Non-Gaussian Closure Techniques     96
Bibliography Notes     100
References     100
Statistical Linearization of Stochastic Dynamic Systems Under External Excitations     103
Moment Criteria     103
Criteria in Probability Density Functions Space     118
Stationary Gaussian Excitations     123
Nonstationary Gaussian Excitations     125
Non-Gaussian Excitations     132
Bibliography Notes     137
References     142
Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation     147
Introduction     147
Moment Criteria     147
Criteria in Probability Density Space     167
Criteria in Spectral Density Space     174
Multi-criterial Linearization Methods     187
Special Linearization Methods     194
Bibliography Notes     201
References      204
Nonlinearization Methods     211
Introduction     211
Moment Criteria     214
Probability Density Criteria     226
Application of the Generalized Stationary Potential Approach     229
Application of Stochastic Averaging Approach     235
Application of Volterra Functional Series Approach     240
Bibliography Notes     246
References     247
Linearization of Dynamic Systems with Stochastic Parametric Excitations     251
Introduction     251
Statistical Linearization     251
Equivalent Linearization     258
Bibliography Notes     278
References     279
Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures     281
Introduction     281
Applications in Hysteretic Systems     282
Vibrations of Structures under Earthquake Excitations     293
Vibrations of Structures Under Wave Excitations     303
Vibrations of Structures Under Wind Excitations     307
Applications in Control Problems     308
Bibliography Notes     328
References     335
Accuracy of Linearization Methods      341
Theoretical Study of the Accuracy of Linearization Methods     341
Comparison of Linearized and Exact Response Characteristics     353
Comparison of Linearized and Simulated Response Characteristics     356
Validation of Linearization Method by Experiments     359
Limitations of Applicability of Linearization Methods     365
Bibliography Notes     367
References     370
Index     377