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