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" Nonlinear dynamics and stochastic mechanics / "
edited by Wolfgang Kliemann, Ph.D., Professor, Department of Mathematics, Iowa State University, Ames, Iowa, N. Sri Namachchivaya, Ph.D., Associate Professor, Department of Aeronautical and Astronautical Engineering, University of Illinois, Urbana-Champaign, Illinois.
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BL
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844272
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| Title & Author
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Nonlinear dynamics and stochastic mechanics /\ edited by Wolfgang Kliemann, Ph.D., Professor, Department of Mathematics, Iowa State University, Ames, Iowa, N. Sri Namachchivaya, Ph.D., Associate Professor, Department of Aeronautical and Astronautical Engineering, University of Illinois, Urbana-Champaign, Illinois.
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| Publication Statement
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Boca Raton :: CRC Press, Taylor & Francis Group,, [2018]
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, ©1995
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| Series Statement
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CRC revivals
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1 online resource.
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| ISBN
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1351075055
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: 1351083503
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: 1351091956
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: 9781351075053
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: 9781351083508
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: 9781351091954
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1315895951
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9781315895956
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9781351083508 (PDF ebook)
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9781351100403 (Mobipocket ebook)
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| Notes
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"First published 1995 by CRC Press"--Copyright page.
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Cover -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- List of Figures -- Preface -- 1: Rotordynamics -- 1.1 Introduction -- 1.2 Rigid Rotors -- 1.3 Deformable Rotors -- 1.4 Rotordynamic Instability -- 1.5 Rotor Asymmetry -- 1.6 Rotor Damping -- 1.7 Fluid Film Bearings -- 1.8 Propeller-Engine Whirl -- 1.9 Whirling Of Rotors Partially Filled With Liquid -- 1.10 Computer Memory Storage Disk -- 1.11 Conclusion -- 1.12 Acknowledgment -- 1.13 References -- 2: Domain-to-Domain Evolution by Cell Mapping -- 2.1 Introduction -- 2.2 Cell State Space and Cell-to-Cell Mapping -- 2.2.1 Simple cell mapping (SCM) -- 2.2.2 Generalized cell mapping (GCM) -- 2.3 Methods to Generate a GCM -- 2.3.1 Sampling method -- 2.3.2 Short-time Gaussian approximation method -- 2.4 Markov Chains -- 2.4.1 Persistent groups -- 2.4.2 Evolution from transient cells -- 2.5 Nested and Cascade Structure of a Markov Chain -- 2.5.1 Domicile-based partition of the transition cells -- 2.5.2 Inner structure of each partitioned Q -- 2.5.3 Upper triangular block matrix form for Q -- 2.6 A Domain-to-Domain Global Transient Analysis -- 2.7 Recent Literature on Cell-to-Cell Mapping -- 2.8 References -- 3: On Internal Resonances in Mechanical Systems -- 3.1 Introduction -- 3.2 Systems With Cubic Nonlinearities -- 3.3 Systems With 3:1 Internal Resonance -- 3.4 Systems With 1:1 Internal Resonance -- 3.5 Acknowledgments -- 3.6 References -- 4: Normal Modes and Modal Analysis Techniques for Nonlinear Structural Systems -- 4.1 Background and Introduction -- 4.2 Individual Normal Modes of Nonlinear Systems: General Case -- 4.3 Individual Normal Modes of Nonlinear Systems: Conservative Systems -- 4.4 Example: An Euler-Bernoulli Beam with a Nonlinear Spring Attached at the Mid-Point -- 4.5 Current Work: Modal Analysis for Nonlinear Systems . -- 4.6 Closing -- 4.7 Acknowledgments.
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12.3 External Excitation at an Interface of Two Cells -- 12.3.1 Monte Carlo simulation -- 12.3.2 Disordered chain with a small number of cells -- 12.4 External Excitation at an Interior Point of a Cell -- 12.5 A Disordered Multi-Span Beam -- 12.6 Conclusion -- 12.7 References -- 13: A Unified Approach to Stochastic Stability -- 13.1 Formulation and Preliminary Results -- 13.2 Stochastic Stability for Itô Systems -- 13.2.1 The Hasminskii condition -- 13.2.2 The method of reduction for equations in a half-space -- 13.2.3 Spiraling properties of two-dimensional systems -- 13.3 Stochastic Stability for the General System -- 13.3.1 Lyapunov exponents and the adjoint method -- 13.3.2 Perturbation scheme -- 13.4 Application to a Single Harmonic Oscillator -- 13.4.1 The underdamped case -- 13.4.2 Comparison of real noise vs. white noise results -- 13.4.3 The critically damped case and related free-particle systems -- 13.4.4 The overdamped oscillator -- 13.5 Application to Coupled Harmonic Oscillators -- 13.5.1 Perturbation scheme -- 13.5.2 White noise calculation -- 13.5.3 Real noise calculation -- 13.6 Lyapunov Exponent of a Stochastic Wave Equation -- 13.7 Summary -- 13.8 Acknowledgments -- 13.9 References -- 14: Stability of an SDOF System under Periodic Parametric Excitation with a White Noise Phase Modulation -- 14.1 Introduction -- 14.2 Stability In Probability -- 14.3 Two Limiting Cases -- 14.4 Numerical Results: Generalized Ince-Strutt Chart -- 14.5 Analysis Of Mean Square Stability -- 14.6 Conclusion -- 14.7 References -- 15: Fatigue Crack Propagation in Random Media -- 15.1 Introduction -- 15.2 Analytical Fracture Mechanics -- 15.3 Theory of Fatigue Fracture -- 15.4 Randomization of Mechanical Properties -- 15.5 Simulation of Fatigue Crack Growth -- 15.6 Conclusion -- 15.7 Acknowledgment -- 15.8 References.
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16: The Role of Stochastic Dynamics in Risk and Reliability Assessment of Structures and Mechanical Systems -- 16.1 Introduction -- 16.2 Reliability Prediction for MDOF-Systems under Stochastic Dynamic Excitation -- 16.2.1 General remarks -- 16.2.2 Nonlinear equation of motion -- 16.2.3 Methods based on the Fokker-Planck equation -- 16.3 Equivalent linearization -- 16.3.1 General remarks -- 16.3.2 The conventional EQL procedure applied to hysteretic systems -- 16.3.3 Non-Gaussian closure by EQL -- 16.3.4 Response surface method -- 16.3.5 Monte Carlo simulation -- 16.3.6 Advanced simulation procedures -- 16.3.7 Numerical example -- 16.4 Discussion and outlook -- 16.5 Acknowledgment -- 16.6 References -- 17: Inelastic Structures under Nonstationary Random Excitation -- 17.1 Introduction -- 17.2 Modelling of the Excitation -- 17.3 Modelling of the Inelastic System -- 17.4 Random Vibration Analysis -- 17.5 Application to Safety Evaluation -- 17.6 Summary and Conclusions -- 17.7 Acknowledgment -- 17.8 References -- 18: Numerical Methods for Stochastic Differential Equations -- 18.1 Introduction -- 18.2 Discrete Time Approximation of SDEs -- 18.3 Convergence Criteria -- 18.4 Stochastic Taylor Expansions -- 18.5 Taylor Schemes -- 18.6 Strong Runge-Kutta-Type Schemes -- 18.7 Weak Runge-Kutta-Type and Extrapolation Schemes -- 18.8 Visualization of Stochastic Dynamics -- 18.9 Lyapunov Exponents -- 18.10 Stochastic Stability and Bifurcation -- 18.11 References -- 19: Computational Methods for Lyapunov Exponents and Invariant Measures -- 19.1 Introduction -- 19.2 Oscillator with Constant Coefficients -- 19.3 Parametric Excitation by Bounded Noise -- 19.4 Iterative Solvers of Parabolic Equations -- 19.5 Analytical Solution of the Fokker-Planck Equation -- 19.6 References -- 20: Stochastic Wave Propagation Recent Trends and New Results -- 20.1 Introduction.
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4.8 References -- 5: Stability Analysis of Symmetric Mechanical Systems -- 5.1 Introduction -- 5.2 Some Properties of Lie Groups -- 5.3 Application of Equivariant Bifurcation Theory -- 5.3.1 General remarks -- 5.3.2 Fluid conveying viscoelastic tube -- 5.3.3 Stability boundary -- 5.3.4 Equivariant bifurcation equations -- 5.3.5 Stationary solutions and their symmetry properties -- 5.4 Stability of Relative Equilibria -- 5.4.1 General remarks -- 5.4.2 Stability of the relative equilibria of a dumbbell satellite -- 5.5 Acknowledgment -- 5.6 References -- 6: Feedback Control of Bifurcation and Chaos in Dynamical Systems -- 6.1 Introduction -- 6.2 Control and Nonlinear Dynamics -- 6.2.1 Nonlinear dynamics of control systems -- 6.2.2 Control of nonlinear dynamics -- 6.3 Bifurcation Control -- 6.3.1 Local static state feedback stabilization -- 6.3.2 Dynamic feedback in bifurcation control -- 6.3.3 Control of period doubling bifurcations -- 6.4 Control of Routes to Chaos -- 6.5 Concluding Remarks -- 6.6 Acknowledgments -- 6.7 References -- 7: On the Discretization of Weakly Nonlinear Spatially Continuous Systems -- 7.1 Introduction -- 7.2 Primary Resonance of a Hinged-Hinged Beam Resting on a Nonlinear Foundation -- 7.2.1 Discretization -- 7.2.2 Direct approach -- 7.3 Parametrically Excited Surface Waves in a Rectangular Container -- 7.4 Nonlinear Response of a Relief Valve -- 7.4.1 Primary resonance -- 7.4.2 Subharmonic resonance of order one-half -- 7.5 Internal Resonance in a Cable -- 7.5.1 Direct approach -- 7.5.2 Discretization -- 7.6 Nonlinear Modes of a System with Quadratic and Cubic Nonlinearities -- 7.6.1 Direct approach -- 7.6.2 Discretization -- 7.7 Conclusion -- 7.8 Acknowledgment -- 7.9 References -- 7.10 Appendices -- 8: Generation of Random Dynamical Systems -- 8.1 Deterministic and Random Dynamical Systems -- 8.1.1 Metric dynamical systems.
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| Abstract
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Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.
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| Subject
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Mechanics, Applied.
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Nonlinear mechanics.
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Stochastic processes.
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Mechanics, Applied.
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Nonlinear mechanics.
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Stochastic processes.
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TECHNOLOGY ENGINEERING / Engineering (General)
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TECHNOLOGY ENGINEERING / Reference.
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| Dewey Classification
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620.1/04
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| LC Classification
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TA350
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| Added Entry
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Kliemann, Wolfgang
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Namachchivaya, N. Sri, (Navaratnam Sri),1957-
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