Nonlinear Dynamics and Stochastic Mechanics

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.

1. Rotordynamics 2. Domain-to-Domain Evolution by Cell Mapping 3. On Internal Resonances of Mechanical Systems 4. Normal Modes and and Modal Analysis Techniques for Nonlinear Structural Systems 5. Stability Analysis of Symmetric Mechanical Systems 6. Feedback Control of Bifurcation and Chaos in Dynamical Systems 7. On the Discretization of Weakly Nonlinear Spatially Continuous Systems 8. Generation of Random Dynamical Systems 9. White Noise Processes in Random Vibration 10. Some Results in Stochastic Linearization of Nonlinear Systems 11. Some Exact Solutions in the Theory of Nonlinear Random Oscillations 12. Response Variation of Disordered Periodic Structures 13. A Unified Approach to Stochastic Stability 14. Stability of an SDOF System under Periodic Parametric Excitation with a White Noise Phase Modulation 15. Fatigue Crack Propagation in Random Media 16. The Role of Stochastic Dynamics in Risk and Reliability Assessment of Structural and Mechanical Systems 17. Inelastic Structures under Nonstationary Random Excitation 18. Numerical Methods for Stochastic Differential Equations 19. Computational Methods for Lyapunov Exponents and Invariant Measures 20. Stochastic Wave Propagation: Recent Trends and New Results

Wolfgang Kliemann