| Preface to the Dover Edition | p. xi |
| Preface | p. xiii |
| Introduction | |
| Random vibration | p. 1 |
| Importance of non-linearities | p. 3 |
| Non-linear random vibration problems | p. 4 |
| Methods of solution | p. 5 |
| Statistical linearization | p. 5 |
| Moment closure | p. 8 |
| Equivalent non-linear equations | p. 9 |
| Perturbation and functional series | p. 9 |
| Markov methods | p. 10 |
| Monte Carlo simulation | p. 11 |
| Role of statistical linearization | p. 12 |
| Scope of book | p. 13 |
| Plan of book | p. 14 |
| General equations of motion and the representation of non-linearities | |
| Introduction | p. 17 |
| The general equations of motion | p. 17 |
| Small vibrations | p. 21 |
| Large vibrations | p. 24 |
| Non-linear conservative forces | p. 25 |
| Motion in a gravitational field | p. 26 |
| Restoring moments for floating bodies | p. 28 |
| Elastic restoring forces | p. 29 |
| Non-linear elasticity | p. 32 |
| Geometric non-linearities | p. 37 |
| Non-linear dissipative forces | p. 39 |
| Internal damping in materials | p. 42 |
| Mathematical representation of hysteresis loops | p. 49 |
| Interface damping | p. 53 |
| Flow induced forces | p. 57 |
| Probability theory and stochastic processes | |
| Introduction | p. 63 |
| Random events and probability | p. 63 |
| Random variables | p. 64 |
| Probability distributions | p. 65 |
| Transformation of random variables | p. 66 |
| Expectation of random variables | p. 67 |
| The Gaussian distribution | p. 70 |
| Properties of Gaussian random variables | p. 72 |
| Expansions of the Gaussian distribution | p. 72 |
| The concept of a stochastic process | p. 75 |
| The complete probabilistic specification | p. 76 |
| The Gaussian process | p. 77 |
| Stationary processes | p. 78 |
| Differentiation of stochastic processes | p. 79 |
| Integration of stochastic processes | p. 80 |
| Ergodicity | p. 80 |
| Spectral decomposition | p. 82 |
| Specification of joint processes | p. 86 |
| Elements of linear random vibration theory | |
| Introduction | p. 88 |
| General input-output relationships | p. 88 |
| Stochastic input-output relationships | p. 90 |
| Analysis of lumped parameter systems | p. 93 |
| Response prediction | p. 93 |
| Free undamped motion | p. 94 |
| Classical modal analysis | p. 95 |
| State variable formulation | p. 97 |
| Complex modal analysis | p. 100 |
| Stochastic response of linear systems | p. 101 |
| Single degree of freedom systems | p. 101 |
| Two degree of freedom systems | p. 107 |
| Multi-degree of freedom systems | p. 111 |
| State variable analysis | p. 113 |
| Analysis using complex modes | p. 115 |
| Statistical linearization for simple systems with stationary response | |
| Introduction | p. 122 |
| Non-linear elements without memory | p. 122 |
| Statistical linearization procedure | p. 123 |
| Optimum linearization | p. 125 |
| Examples | p. 126 |
| Oscillators with non-linear stiffness | p. 129 |
| The statistical linearization approximation | p. 131 |
| Standard deviation of the response | p. 133 |
| The case of small non-linearity | p. 136 |
| Power spectrum of the response | p. 137 |
| Inputs with non-zero means | p. 137 |
| Asymmetric non-linearities | p. 140 |
| Systems with a softening restoring characteristic | p. 144 |
| Systems with multiple static equilibrium positions | p. 147 |
| Response to narrow-band excitation | p. 151 |
| Oscillators with non-linear stiffness and damping | p. 155 |
| Standard deviation of the response | p. 158 |
| The case of small non-linearity | p. 160 |
| Power spectrum of the response | p. 161 |
| Input and output with non-zero means | p. 161 |
| Higher order linearization | p. 162 |
| Applications | p. 164 |
| Friction controlled slip of a structure on a foundation | p. 164 |
| Ship roll motion in irregular waves | p. 168 |
| Flow induced vibration of cylindrical structures | p. 173 |
| Statistical linearization of multi-degree of freedom systems with stationary response | |
| Introduction | p. 177 |
| The non-linear system | p. 177 |
| The equivalent linear system | p. 178 |
| Formulation | p. 178 |
| Minimization procedure | p. 179 |
| Equations for the equivalent linear system parameters | p. 179 |
| Examination of the minimum | p. 181 |
| Existence and uniqueness of the equivalent linear system | p. 182 |
| Mechanization of the method | p. 183 |
| Determination of the elements of the equivalent linear system | p. 184 |
| Gaussian approximation | p. 184 |
| Chain-like systems | p. 185 |
| Treatment of asymmetric non-linearities | p. 186 |
| Solution procedures | p. 187 |
| General remarks | p. 187 |
| Spectral matrix solution procedure | p. 188 |
| Modal analysis | p. 196 |
| State variable solution procedure | p. 202 |
| Complex modal analysis | p. 205 |
| Mode-by-mode linearization | p. 209 |
| Non-stationary problems | |
| Introduction | p. 212 |
| General theory | p. 212 |
| White noise excitation | p. 216 |
| Friction controlled slip of a structure on a foundation | p. 217 |
| Oscillator with asymmetric non-linearity | p. 222 |
| Non-white excitation | p. 225 |
| Decomposition method | p. 226 |
| Use of pre-filters | p. 227 |
| An example | p. 230 |
| Systems with hysteretic non-linearity | |
| Introduction | p. 235 |
| Averaging method | p. 235 |
| An alternative approach | p. 239 |
| Evaluation of the expectations | p. 241 |
| Application to non-hysteretic oscillators | p. 243 |
| Inputs with non-zero means | p. 245 |
| The bilinear oscillator | p. 246 |
| Allowance for drift motion | p. 255 |
| Use of differential models of hysteresis | p. 257 |
| Oscillators with hysteresis | p. 257 |
| The bilinear oscillator | p. 264 |
| The curvilinear model | p. 271 |
| Inputs with non-zero means | p. 273 |
| Biaxial hysteretic restoring forces | p. 275 |
| Multi-degree of freedom systems | p. 276 |
| Non-stationary problems | p. 281 |
| Degrading systems | p. 281 |
| Non-stationary excitation | p. 284 |
| Relaxation of the Gaussian response assumption | |
| Introduction | p. 285 |
| Statistical linearization and Gaussian closure | p. 285 |
| An example | p. 289 |
| Non-Gaussian closure | p. 293 |
| Moment equations | p. 293 |
| Closure techniques | p. 295 |
| An example | p. 297 |
| Method of equivalent non-linear equations (ENLE) | p. 307 |
| Exact solution | p. 308 |
| Equivalent non-linear equations | p. 311 |
| Oscillators with linear stiffness and non-linear damping | p. 314 |
| Oscillators with quadratic damping | p. 316 |
| Oscillators with linear-plus-cubic damping | p. 318 |
| An alternative approach | p. 321 |
| Reliability estimation | p. 324 |
| First passage probability | p. 324 |
| Fatigue life | p. 326 |
| An example | p. 328 |
| Parametric identification | p. 332 |
| Direct optimization | p. 335 |
| State variable filters | p. 336 |
| An example | p. 339 |
| Accuracy of statistical linearization | |
| Introduction | p. 347 |
| Exact solutions | p. 347 |
| Linear damping | p. 348 |
| Chain-like systems | p. 349 |
| First-order systems | p. 352 |
| Comparison with exact solutions | p. 352 |
| First-order systems | p. 352 |
| Oscillators with power-law springs | p. 353 |
| Duffing oscillators | p. 355 |
| Oscillators with tangent-law springs | p. 357 |
| Oscillators with non-linear damping | p. 359 |
| Comparison with Monte Carlo simulation results | p. 361 |
| Simulation technique | p. 361 |
| Oscillators with non-linear damping | p. 363 |
| Oscillators with non-linear springs | p. 366 |
| Oscillators with hysteresis | p. 371 |
| Multi-degree of freedom systems with hysteresis | p. 375 |
| Non-stationary response | p. 376 |
| Concluding remarks | p. 378 |
| Evaluation of expectations | p. 380 |
| A useful integral for random vibration analyses | p. 382 |
| Addendum to Appendix B | p. 387 |
| References | p. 393 |
| Additional References | p. 405 |
| Author index | p. 438 |
| Subject index | p. 442 |
| Table of Contents provided by Ingram. All Rights Reserved. |
