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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 | |