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| Preface to the Dover Edition | |
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| Preface | |
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| Introduction | |
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| Random vibration | |
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| Importance of non-linearities | |
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| Non-linear random vibration problems | |
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| Methods of solution | |
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| Statistical linearization | |
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| Moment closure | |
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| Equivalent non-linear equations | |
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| Perturbation and functional series | |
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| Markov methods | |
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| Monte Carlo simulation | |
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| Role of statistical linearization | |
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| Scope of book | |
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| Plan of book | |
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| General equations of motion and the representation of non-linearities | |
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| Introduction | |
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| The general equations of motion | |
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| Small vibrations | |
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| Large vibrations | |
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| Non-linear conservative forces | |
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| Motion in a gravitational field | |
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| Restoring moments for floating bodies | |
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| Elastic restoring forces | |
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| Non-linear elasticity | |
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| Geometric non-linearities | |
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| Non-linear dissipative forces | |
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| Internal damping in materials | |
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| Mathematical representation of hysteresis loops | |
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| Interface damping | |
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| Flow induced forces | |
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| Probability theory and stochastic processes | |
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| Introduction | |
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| Random events and probability | |
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| Random variables | |
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| Probability distributions | |
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| Transformation of random variables | |
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| Expectation of random variables | |
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| The Gaussian distribution | |
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| Properties of Gaussian random variables | |
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| Expansions of the Gaussian distribution | |
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| The concept of a stochastic process | |
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| The complete probabilistic specification | |
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| The Gaussian process | |
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| Stationary processes | |
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| Differentiation of stochastic processes | |
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| Integration of stochastic processes | |
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| Ergodicity | |
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| Spectral decomposition | |
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| Specification of joint processes | |
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| Elements of linear random vibration theory | |
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| Introduction | |
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| General input-output relationships | |
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| Stochastic input-output relationships | |
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| Analysis of lumped parameter systems | |
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| Response prediction | |
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| Free undamped motion | |
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| Classical modal analysis | |
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| State variable formulation | |
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| Complex modal analysis | |
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| Stochastic response of linear systems | |
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| Single degree of freedom systems | |
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| Two degree of freedom systems | |
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| Multi-degree of freedom systems | |
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| State variable analysis | |
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| Analysis using complex modes | |
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| Statistical linearization for simple systems with stationary response | |
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| Introduction | |
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| Non-linear elements without memory | |
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| Statistical linearization procedure | |
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| Optimum linearization | |
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| Examples | |
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| Oscillators with non-linear stiffness | |
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| The statistical linearization approximation | |
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| Standard deviation of the response | |
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| The case of small non-linearity | |
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| Power spectrum of the response | |
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| Inputs with non-zero means | |
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| Asymmetric non-linearities | |
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| Systems with a softening restoring characteristic | |
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| Systems with multiple static equilibrium positions | |
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| Response to narrow-band excitation | |
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| Oscillators with non-linear stiffness and damping | |
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| Standard deviation of the response | |
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| The case of small non-linearity | |
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| Power spectrum of the response | |
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| Input and output with non-zero means | |
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| Higher order linearization | |
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| Applications | |
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| Friction controlled slip of a structure on a foundation | |
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| Ship roll motion in irregular waves | |
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| Flow induced vibration of cylindrical structures | |
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| Statistical linearization of multi-degree of freedom systems with stationary response | |
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| Introduction | |
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| The non-linear system | |
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| The equivalent linear system | |
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| Formulation | |
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| Minimization procedure | |
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| Equations for the equivalent linear system parameters | |
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| Examination of the minimum | |
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| Existence and uniqueness of the equivalent linear system | |
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| Mechanization of the method | |
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| Determination of the elements of the equivalent linear system | |
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| Gaussian approximation | |
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| Chain-like systems | |
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| Treatment of asymmetric non-linearities | |
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| Solution procedures | |
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| General remarks | |
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| Spectral matrix solution procedure | |
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| Modal analysis | |
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| State variable solution procedure | |
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| Complex modal analysis | |
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| Mode-by-mode linearization | |
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| Non-stationary problems | |
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| Introduction | |
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| General theory | |
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| White noise excitation | |
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| Friction controlled slip of a structure on a foundation | |
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| Oscillator with asymmetric non-linearity | |
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| Non-white excitation | |
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| Decomposition method | |
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| Use of pre-filters | |
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| An example | |
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| Systems with hysteretic non-linearity | |
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| Introduction | |
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| Averaging method | |
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| An alternative approach | |
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| Evaluation of the expectations | |
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| Application to non-hysteretic oscillators | |
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| Inputs with non-zero means | |
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| The bilinear oscillator | |
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| Allowance for drift motion | |
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| Use of differential models of hysteresis | |
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| Oscillators with hysteresis | |
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| The bilinear oscillator | |
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| The curvilinear model | |
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| Inputs with non-zero means | |
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| Biaxial hysteretic restoring forces | |
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| Multi-degree of freedom systems | |
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| Non-stationary problems | |
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| Degrading systems | |
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| Non-stationary excitation | |
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| Relaxation of the Gaussian response assumption | |
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| Introduction | |
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| Statistical linearization and Gaussian closure | |
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| An example | |
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| Non-Gaussian closure | |
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| Moment equations | |
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| Closure techniques | |
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| An example | |
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| Method of equivalent non-linear equations (ENLE) | |
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| Exact solution | |
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| Equivalent non-linear equations | |
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| Oscillators with linear stiffness and non-linear damping | |
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| Oscillators with quadratic damping | |
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| Oscillators with linear-plus-cubic damping | |
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| An alternative approach | |
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| Reliability estimation | |
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| First passage probability | |
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| Fatigue life | |
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| An example | |
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| Parametric identification | |
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| Direct optimization | |
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| State variable filters | |
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| An example | |
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| Accuracy of statistical linearization | |
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| Introduction | |
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| Exact solutions | |
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| Linear damping | |
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| Chain-like systems | |
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| First-order systems | |
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| Comparison with exact solutions | |
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| First-order systems | |
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| Oscillators with power-law springs | |
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| Duffing oscillators | |
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| Oscillators with tangent-law springs | |
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| Oscillators with non-linear damping | |
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| Comparison with Monte Carlo simulation results | |
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| Simulation technique | |
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| Oscillators with non-linear damping | |
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| Oscillators with non-linear springs | |
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| Oscillators with hysteresis | |
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| Multi-degree of freedom systems with hysteresis | |
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| Non-stationary response | |
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| Concluding remarks | |
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| Evaluation of expectations | |
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| A useful integral for random vibration analyses | |
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| Addendum to Appendix B | |
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| References | |
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| Additional References | |
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| Author index | |
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| Subject index | |