Ebook: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics: Proceedings of the IUTAM Symposium held in Ithaca, NY, U.S.A., 27 July–1 August 1997

It is two decades since Mitchell Feigenbaum's landmark papers on period doubling and the modern beginnings of what is now called "Chaos Theory". From the very beginning, mechanics has been a central focus for modem nonlinear dynamical systems. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the new chaos theory a mark of credibility, importance, and relevance that its earlier sister field, catastrophe theory, did not achieve. The fact that mechanics straddles both physics and engineering also meant that mechanics became a pathway for direct application of chaos theory to applied problems. So what is new in nonlinear dynamics and mechanics today? First the scope of applications in solid mechanics has broadened to cover material processing, inelasticity and fracture mechanics. In rigid body dynamics, more complex systems such as vehicles, robotics and controlled machines have come into the purview of nonlinear dynamicists. On the mathematics side of nonlinear dynamics, it is now recognized that spatio-temporal problems, hysteretic and time delay problems are the new frontiers in this field. Also the term "complexity" has been added to the lexicon of chaos theory to describe the dynamics of many interacting sub systems which can exhibit self organization and evolution. Complexity analysis has gained a foothold in biological and some social sciences as well in fluid and chemical physics.

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Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Bifurcation in Stochastically Perturbed Dynamical Systems....Pages 3-11
Nonstationary Responses in Two Degree-of-Freedom Nonlinear Systems with 1-to-2 Internal Resonance....Pages 13-22
Sinusoidally Varying Period-Doubling Bifurcations....Pages 23-29
Wavelet Approach to Mechanical Problems. Symplectic Group, Symplectic Topology and Symplectic Scales....Pages 31-40
On the Generalized Cell Mapping....Pages 41-50
Bursts....Pages 51-60
Dynamics of a Quasiperiodically-Forced Mathieu Oscillator....Pages 61-70
Improved Galerkin Method in the Dimension Reduction of Nonlinear Dynamical Systems....Pages 71-80
Sequences of Global Bifurcations and Multiple Chaotic Transients in a Mechanical Driven Oscillator....Pages 81-91
Bifurcation of Homoclinic Orbits in Autonomous Systems and in Chaotic Blue Sky Catastrophe....Pages 93-100
Wavelet Approach to Polynomial Mechanical Problems....Pages 101-108
Jumps to Resonance Phenomena in Nonlinear Mechanics: Fractal Basins, Chaotic Transients and Unpredictability....Pages 109-115
Global Stable Oscillations Near Unstable Equilibrium Positions: The Hilltop Effect....Pages 117-124
Front Matter....Pages 125-125
Homoclinic Orbits, Spatial Chaos and Localized Buckling....Pages 127-138
Nonregular Regimes of Monodimensional Mechanical Systems with Initial Curvature: Experiments and Time Series Analysis....Pages 139-148
Constrained Euler Buckling: Line Contact Solutions....Pages 149-158
The Role of Homoclinic Bifurcations in Understanding the Buckling of Long Thin Cylindrical Shells....Pages 159-168
Dynamics of a Buckled Drillstring Rotating in a Curved Oil Wellbore....Pages 169-171
The Complex Non-Linear Dynamics of Imperfection Sensitive Shells....Pages 173-180
Front Matter....Pages 181-181
The Dynamics of Chip Formation in Machining....Pages 183-192
Front Matter....Pages 181-181
Chatter Identification and Control for a Boring Process....Pages 193-202
Coupling and Resonance Phenomena in Dynamic Systems with Hysteresis....Pages 203-212
Maps, Traps, and Equilibria for a Fully Dissipative Elastoplastic Oscillator....Pages 213-220
Front Matter....Pages 221-221
Nonlinear Dynamics and the Design of Tuned Pendulum Vibration Absorbers....Pages 223-234
Dynamical Behavior of Chains....Pages 235-252
Chaos in Offset Hydrodynamic Rotor Bearings....Pages 253-260
Front Matter....Pages 261-261
Dynamics of Elastic Structures Subjected to Impact Excitations....Pages 263-272
A Method for Finding all Possible Periodic Orbits in Piecewise Continuous Mechanical Systems of Arbitrary Dimension....Pages 273-282
Dynamics of the Impact Oscillator....Pages 283-292
Numerical and Experimental Investigation of Nonsmooth Mechanical Systems....Pages 293-302
Steady-State Behaviour of a Solar Array System with Elastic Stops....Pages 303-312
Nonlinear Dynamics of Mechanical Systems with Discontinuities....Pages 313-322
Displacement Potentials in Non-Smooth Dynamics....Pages 323-330
Front Matter....Pages 331-331
Driven Nonlinear Oscillators for Modeling Cardiac Phenomena....Pages 333-342
Chaos, Synchronization and Bifurcations in a Driven R-L-Diode Circuit....Pages 343-352
Transient Global Behavior in Nonlinear Experimental Oscillators....Pages 353-362
Control of Chaos for Pendulum Systems....Pages 363-370
Front Matter....Pages 371-371
Delay, Nonlinear Oscillations and Shimmying Wheels....Pages 373-386
Symmetry, Generic Bifurcations, and Mode Interaction in Nonlinear Railway Dynamics....Pages 387-396
A Traveler’s Woes: Some Perspectives from Dynamical Systems....Pages 397-406
Front Matter....Pages 371-371
Stability and Chaos in Passive-Dynamic Locomotion....Pages 407-416
On the Multi-Degree of Freedom, Nonlinear Dynamics of Ship Motions with Application to the Broaching Problem....Pages 417-424
Front Matter....Pages 425-425
Nonlinear Dynamics of Aeroelastic Systems....Pages 427-449
Stabilization of Nonlinear Hydroelastic Structures via Random Parametric Excitation....Pages 451-460
Aircraft Stability and Control: Bifurcation Analysis In The Design Process?....Pages 461-470
Global Dynamics in Gyroscopic and Aeroelastic Systems....Pages 471-482
Chaotic Oscillations of a Loosely Supported Tube in a Heat-Exchanger Array in Cross-Flow....Pages 483-492
Stabilization of Periodic Flap-Lag Dynamics in Rotorcraft....Pages 493-502
A Mathematical Model of Pendelluft Flow in a Single Airway Bifurcation....Pages 503-504
The Periodic to Chaotic Water Wheel....Pages 505-512
Helical Waves and Nonlinear Dynamics of Fluid/Structure Interactions in a Cylinder Row....Pages 513-520
Front Matter....Pages 521-521
Spatio-Temporal Dynamics of Coupled Magneto-Elastic System....Pages 523-531
Spatially Localized and Chaotic Motions of a Discretely Supported Elastic Continuum....Pages 533-542
Optimal Control of Spatiotemporal Chaos in Coupled Map Lattices....Pages 543-550
Back Matter....Pages 551-562

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Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Bifurcation in Stochastically Perturbed Dynamical Systems....Pages 3-11
Nonstationary Responses in Two Degree-of-Freedom Nonlinear Systems with 1-to-2 Internal Resonance....Pages 13-22
Sinusoidally Varying Period-Doubling Bifurcations....Pages 23-29
Wavelet Approach to Mechanical Problems. Symplectic Group, Symplectic Topology and Symplectic Scales....Pages 31-40
On the Generalized Cell Mapping....Pages 41-50
Bursts....Pages 51-60
Dynamics of a Quasiperiodically-Forced Mathieu Oscillator....Pages 61-70
Improved Galerkin Method in the Dimension Reduction of Nonlinear Dynamical Systems....Pages 71-80
Sequences of Global Bifurcations and Multiple Chaotic Transients in a Mechanical Driven Oscillator....Pages 81-91
Bifurcation of Homoclinic Orbits in Autonomous Systems and in Chaotic Blue Sky Catastrophe....Pages 93-100
Wavelet Approach to Polynomial Mechanical Problems....Pages 101-108
Jumps to Resonance Phenomena in Nonlinear Mechanics: Fractal Basins, Chaotic Transients and Unpredictability....Pages 109-115
Global Stable Oscillations Near Unstable Equilibrium Positions: The Hilltop Effect....Pages 117-124
Front Matter....Pages 125-125
Homoclinic Orbits, Spatial Chaos and Localized Buckling....Pages 127-138
Nonregular Regimes of Monodimensional Mechanical Systems with Initial Curvature: Experiments and Time Series Analysis....Pages 139-148
Constrained Euler Buckling: Line Contact Solutions....Pages 149-158
The Role of Homoclinic Bifurcations in Understanding the Buckling of Long Thin Cylindrical Shells....Pages 159-168
Dynamics of a Buckled Drillstring Rotating in a Curved Oil Wellbore....Pages 169-171
The Complex Non-Linear Dynamics of Imperfection Sensitive Shells....Pages 173-180
Front Matter....Pages 181-181
The Dynamics of Chip Formation in Machining....Pages 183-192
Front Matter....Pages 181-181
Chatter Identification and Control for a Boring Process....Pages 193-202
Coupling and Resonance Phenomena in Dynamic Systems with Hysteresis....Pages 203-212
Maps, Traps, and Equilibria for a Fully Dissipative Elastoplastic Oscillator....Pages 213-220
Front Matter....Pages 221-221
Nonlinear Dynamics and the Design of Tuned Pendulum Vibration Absorbers....Pages 223-234
Dynamical Behavior of Chains....Pages 235-252
Chaos in Offset Hydrodynamic Rotor Bearings....Pages 253-260
Front Matter....Pages 261-261
Dynamics of Elastic Structures Subjected to Impact Excitations....Pages 263-272
A Method for Finding all Possible Periodic Orbits in Piecewise Continuous Mechanical Systems of Arbitrary Dimension....Pages 273-282
Dynamics of the Impact Oscillator....Pages 283-292
Numerical and Experimental Investigation of Nonsmooth Mechanical Systems....Pages 293-302
Steady-State Behaviour of a Solar Array System with Elastic Stops....Pages 303-312
Nonlinear Dynamics of Mechanical Systems with Discontinuities....Pages 313-322
Displacement Potentials in Non-Smooth Dynamics....Pages 323-330
Front Matter....Pages 331-331
Driven Nonlinear Oscillators for Modeling Cardiac Phenomena....Pages 333-342
Chaos, Synchronization and Bifurcations in a Driven R-L-Diode Circuit....Pages 343-352
Transient Global Behavior in Nonlinear Experimental Oscillators....Pages 353-362
Control of Chaos for Pendulum Systems....Pages 363-370
Front Matter....Pages 371-371
Delay, Nonlinear Oscillations and Shimmying Wheels....Pages 373-386
Symmetry, Generic Bifurcations, and Mode Interaction in Nonlinear Railway Dynamics....Pages 387-396
A Traveler’s Woes: Some Perspectives from Dynamical Systems....Pages 397-406
Front Matter....Pages 371-371
Stability and Chaos in Passive-Dynamic Locomotion....Pages 407-416
On the Multi-Degree of Freedom, Nonlinear Dynamics of Ship Motions with Application to the Broaching Problem....Pages 417-424
Front Matter....Pages 425-425
Nonlinear Dynamics of Aeroelastic Systems....Pages 427-449
Stabilization of Nonlinear Hydroelastic Structures via Random Parametric Excitation....Pages 451-460
Aircraft Stability and Control: Bifurcation Analysis In The Design Process?....Pages 461-470
Global Dynamics in Gyroscopic and Aeroelastic Systems....Pages 471-482
Chaotic Oscillations of a Loosely Supported Tube in a Heat-Exchanger Array in Cross-Flow....Pages 483-492
Stabilization of Periodic Flap-Lag Dynamics in Rotorcraft....Pages 493-502
A Mathematical Model of Pendelluft Flow in a Single Airway Bifurcation....Pages 503-504
The Periodic to Chaotic Water Wheel....Pages 505-512
Helical Waves and Nonlinear Dynamics of Fluid/Structure Interactions in a Cylinder Row....Pages 513-520
Front Matter....Pages 521-521
Spatio-Temporal Dynamics of Coupled Magneto-Elastic System....Pages 523-531
Spatially Localized and Chaotic Motions of a Discretely Supported Elastic Continuum....Pages 533-542
Optimal Control of Spatiotemporal Chaos in Coupled Map Lattices....Pages 543-550
Back Matter....Pages 551-562
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