Vibro-Impact Dynamics (eBook)

Title Page 2
Preface 7
Contents 9
Introduction 12
Modeling and Analytical Approaches 17
Introduction 17
Power-Law Phenomenological Modeling 17
Zhuravlev Non-smooth Coordinate Transformation 20
Ivanov Transformation 23
Hertzian Contact 25
Point-Wise Mapping 32
Saw-Tooth-Time-Transformation 35
Closing Remarks 39
Mapping of Grazing and C–Bifurcations 40
Introduction 40
Grazing Bifurcation 40
Discontinuity Mappings 42
Border–Collision or C–Bifurcation 57
Border Bifurcation in Switching Circuits 61
Closing Remarks 63
Single–Degree–of–Freedom Systems 64
Introduction 64
Bouncing Ball on a Vibrating Platform and Pile Drivers 65
Mass–Spring System 73
Pendulum Oscillating Against One– or Two–Sided Barrier 84
Ship Impact Interaction with Ice 91
Closing Remarks 104
Two– and Multi–Degree–of–Freedom Systems 105
Introduction 105
Two–Degree–of–Freedom Systems 105
Spherical Pendulum under Liquid Flow 116
Pendulum Simulating Liquid Sloshing Impact 120
Multi–Degree–of–Freedom Systems 130
Closing Remarks 131
Non–Classical Lumped Systems 132
Introduction 132
Mechanical Joints 132
Rub–Impact Dynamics of Rotors 135
Micro–Actuators 141
Vocal Folds 144
Vibration Protection under Vibro–Impact 150
Other Applications 152
Closing Remarks 156
Continuous Systems 157
Introduction 157
Strings 157
Beams 161
Constrained Pipes Conveying Liquid 168
Nuclear Reactors and Heat Exchangers 176
Plates 193
Slamming of Ocean Waves 196
Closing Remarks 197
Stochastic Vibro–Impact Dynamics 198
Introduction 198
Beam–Stop under Random Excitation 200
Cantilever Beam with One–Sided Barrier 206
Pre–Loaded Vibro–Impact Hertzian Contact 210
Random Impulsive Excitation 215
Closing Remarks 221
Impact Dampers 222
Introduction 222
Basic Concept and Applications 222
Analogue Computer and Numerical Simulations 225
Analytical Results 226
Experimental Results 229
Random Excitation 231
Design Considerations 234
Semi–Active and Active Control of Impact Dampers 236
Closing Remarks 237
References 238
Index 299