IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty: Proceedings of the IUTAM Symposium held in Nanjing, China, September 18-22, 2006 (IUTAM Bookseries Book 2)

The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain an insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity. However, the new control strategy to be proposed must be robust enough so that any unexpected small disturbances will not alter the desired target of control. Such a concept is calling more attention to the modelling and simplification of dynamic systems subject to uncertain environment, the fine analysis and robust design of controlled dynamic systems based on either good understanding of nonlinear phenomena or artificial intelligence, the combination of passive control, active control and semi-active control, as well as the interaction among sensors, controllers and actuators. Contents......Page 6 Preface......Page 10 Opening Address......Page 17 Welcome Address......Page 20 Part 1 System Modeling With Uncertainty......Page 24 1. Introduction......Page 25 2. Modeling Of Seat-occupant System......Page 27 2.1 Quasi-static Foam Behavior......Page 28 2.2 Modeling Of Interfacial Forces......Page 30 2.3 Equations Of Motion......Page 31 3. Solutions For Static Equilibrium......Page 32 4. Numerical Results And Discussion......Page 33 References......Page 34 1. Introduction......Page 35 2.1 Polynomial Chaos Expansion......Page 36 2.2 Restoring Force Identification......Page 37 2.3 Polynomial Chaos Representation Of Stochastic Inputs......Page 38 2.4 Polynomial Chaos Representation Of Stochastic Outputs......Page 39 3. Application To Sdof Duffing Oscillator......Page 40 4. Summary And Conclusions......Page 45 References......Page 46 1. Introduction......Page 47 2. Modeling Of The System......Page 48 2.2 Environmental Model......Page 49 3. Simulation Concept......Page 52 4. Results......Page 53 5. Conclusions......Page 55 Refere Nces......Page 56 1. Introduction......Page 57 Impacts In Multibody Systems......Page 58 3. Numerical Models......Page 60 4. Essential Parameters For The Coefficient Of Restitution......Page 61 5.1 Comparison Of Numerical Models......Page 63 5.2 Experimental Validation......Page 64 5.3 Analysis Of The Coefficient Of Restitution......Page 66 References......Page 67 Part 2 System Dynamics With Uncertainty......Page 69 1. Introduction......Page 70 2. Subset Simulation Method......Page 72 2.1 Procedure......Page 73 2.2 Data-mining Using Markov Chain Samples......Page 74 Illustrative Applications......Page 75 4. Recent Developments......Page 77 References......Page 78 1. Introduction......Page 80 2.1 Trajectory Tubes To Impulsive Systems......Page 82 2.2 Systems With State Constraints......Page 84 3. Linear Impulsive Systems With Ellipsoidal Constraints......Page 85 Acknowledgements......Page 88 Refere Nces......Page 89 1. Introduction......Page 90 2.1 Random Dynamical Systems......Page 92 2.2 Generation Of Rds From Differential Equations......Page 94 2.3 Invariant And Stationary Measures......Page 95 3.1 Markov Operators......Page 96 3.2 Approximation Of The Markov Operators......Page 97 3.3 Approximation Of Stationary Densities......Page 98 4. Numerical Example......Page 99 5. Conclusions......Page 100 References......Page 101 1. Introduction......Page 102 2. Dynamical Model Of The System......Page 103 3. Result And Discussion......Page 105 Acknowledgements......Page 109 A2. Some Diagrams Of The Undisturbed Case......Page 110 References......Page 111 1. Introduction......Page 112 2. The Spectral Analysis For A Linear Filter System......Page 113 3. Formulation......Page 114 4. Asymptotical Analysis......Page 115 5. Expansion Of Invariant Measure......Page 117 Asymptotic Expansion For Top Lyapunov Exponent......Page 120 References......Page 121 1. Dimensionless Set-up Of The Problem......Page 122 2. Nonstationary Polynomial Moments......Page 124 3. Stability Of Stationary Processes......Page 127 4. Evaluation Of Top Lyapunov Exponents......Page 130 5. Summary And Conclusion......Page 132 References......Page 133 1. Introduction......Page 134 2. Uncertainties Induced By Boundary Crisis And Effect Of Noise To Wada Basin Boundaries......Page 136 3. Control Uncertainty In Duffing Equation......Page 139 References......Page 141 1. Introduction......Page 142 2. How To Approximate The Invariant Manifolds......Page 143 3. Basin Erosion Of Duffing Oscillator Under Deterministic Excitation......Page 144 Basin Erosion Of Duffing Oscillator Under Stochastic Noise......Page 148 5. Conclusions......Page 150 References......Page 151 Part 3 Nonlinear Dynamics......Page 152 1. Introduction......Page 153 2. Direct Problem......Page 157 Inverse Problem......Page 158 4. Random Fractals......Page 160 References......Page 162 1. Introduction......Page 163 2. Ray Theory......Page 164 3. Stability......Page 167 4. Transitions......Page 169 References......Page 172 1. Introduction......Page 173 2. Gea Equation For Deterministic Systems......Page 174 3.1 Free Oscillation Of A Nonlinear Suspension System......Page 175 3.2 Forced Oscillation – Nonlinear Suspension System......Page 179 4. Conclusions......Page 181 References......Page 182 1. Introduction......Page 183 2. Bifurcation Of Single-sided Constraint......Page 184 3. Bifurcation Of Double-sided Constraint......Page 185 4. Periodic Bifurcations Of Non-smooth Systems......Page 187 5. Conclusions......Page 191 References......Page 192 1. Introduction......Page 193 2.1 Typical Equations Of Motion Of Rotor System......Page 194 2.2 Introduction Of Complex Coordinate And Separation Of Forward And Backward Whirling Modes......Page 196 2.3 Application Of The Method Of Multiple Scales To Rotor Dynamics......Page 197 2.4 Production Of Backward Whirling Mode Due To Nonlinearity And Gravity Effect......Page 199 3. Experiment......Page 201 References......Page 202 1. Introduction......Page 203 2. Dynamical Model Of Spur Gear Pair......Page 204 3. Computation Scheme For The Periodic Solutions By Ihbm......Page 205 4. Results And Analysis......Page 208 References......Page 212 1. Introduction......Page 213 2. The Transcription Of The Optimal Control Problem Into A Nlp......Page 216 2.1 Description Of The Algorithm......Page 218 3. Numerical Example......Page 219 4. Discussions And Conclusions......Page 220 References......Page 222 Part 4 Dynamics Of High-dimensional Systems......Page 223 1. Introduction......Page 224 2. Experimental Rig......Page 225 3. Mathematical Modelling......Page 226 4. Numerical Prediction And Experimental Observation......Page 228 5. Concluding Remarks......Page 232 References......Page 233 1. Introduction......Page 234 1.2 Micro-scale Cantilever Arrays......Page 235 2.1 Simulation Profile......Page 237 2.2 Array Model......Page 238 2.3 Analytical Profile......Page 239 3. Results And Discussion......Page 241 Acknowledgements......Page 242 References......Page 243 1. Introduction......Page 244 2. Problem Formulations......Page 245 3. Multi-scale Analysis......Page 246 Steady-state Response......Page 248 5. Stability......Page 250 7. Conclusions......Page 252 References......Page 253 1. Introduction......Page 254 2. Statement Of The Problem......Page 255 3. Relative Motion......Page 256 4. Dry Friction: Two-phase Motion......Page 258 5. Dry Friction: Three-phase Motion......Page 259 6. Generalizations And Experiments......Page 260 7. Nonlinear Resistance......Page 261 References......Page 263 1. Introduction......Page 264 2. Mechanical Model......Page 265 3. Linear Modal Characteristics......Page 266 4. Nonlinear Modal Characteristics......Page 268 Concluding Remarks......Page 271 References......Page 273 1. Introduction......Page 274 2. Mechanical Model And Modal Expansion......Page 276 3. Homoclinic Orbits (unperturbed System)......Page 277 3.1 A Hierarchy Of Roms......Page 278 4. Homoclinic Bifurcations (perturbed System)......Page 280 5.2 Optimizing The Temporal Shape Of The Excitation......Page 282 References......Page 283 1. Introduction......Page 284 2. Mechanical Model With One Degree Of Freedom......Page 285 3. Continuous Infinite Dimensional System......Page 288 References......Page 293 1. Introduction......Page 294 2. Equations Of Motion And Perturbation Analysis......Page 296 4. Dissipative Perturbations......Page 299 5. The K-pulse Melnikov Function......Page 300 7. Conclusions......Page 302 References......Page 303 Part 5 Control Of Nonlinear Dynamic Systems......Page 304 1. Introduction......Page 305 2. Statement Of The Problem......Page 307 3. Synthesis Of Control......Page 308 4. The Computer Simulation Results......Page 311 5. Comparison With Time-optimal Control......Page 313 References......Page 314 1. Introduction......Page 315 2. Physical Model......Page 316 3.1 Boundary Value Problem......Page 317 4. Vibration Suppression Concept......Page 320 4.1 Model Reduction......Page 321 4.3 Full State Observer......Page 322 4.4 Telescopic Operations With Clearance......Page 323 References......Page 324 1. Introduction......Page 325 2. Problem Formulation......Page 327 2.1 Algebraic Non-linear Equations......Page 329 3. Results......Page 330 Acknowledgements......Page 333 Refere Nces......Page 334 1. Introduction......Page 335 2. Model For Aeroservoelastic System......Page 336 3. Model Of Servo......Page 338 4. Design Of Robust Controllers......Page 339 5. Numerical Simulations......Page 341 6. Wind Tunnel Tests......Page 342 References......Page 344 1. Introduction......Page 345 2. The Model......Page 346 3. Synchronization, Periodization And Beating Of The Oscillations......Page 347 References......Page 350 1. Intruduction......Page 351 2. Noise-induced Synchronization......Page 352 2.1 Noise-induced Complete Synchronization......Page 353 2.2 Noise-induced Phase Synchronization......Page 354 3.1 Noise-enhanced Complete Synchronization......Page 355 4. Spatial Patterns In A Square-lattice Hh Neuronal Systems The last decade has witnessed an increasing interest towards the dynamics and control of nonlinear engineering systems from the scientists engaged in nonlinear dynamics and the control engineers. Both groups of people have recognized the importance of interaction between nonlinear dynamics and robust control during their efforts to improve the dynamic performance of engineering systems with uncertainty, which comes from either the random excitations, such as wind and earthquake, or the modelling errors of real systems including their sensors, controllers and actuators. The dynamics and control of nonlinear systems with uncertainty, therefore, is a vital interdisciplinary topic related to both stochastic systems and deterministic systems. This volume contains the papers presented at the IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty, which was sponsored by the International Union of Theoretical and Applied Mechanics (IUTAM) and held at Nanjing University of Aeronautics and Astronautics, China, 18-22 September, 2006. The aim of the symposium was to bringing together the scientists to discuss the advances in dynamics and control of nonlinear systems, especially those with uncertainties in either system modeling or excitation. The scientific committee, appointed by the Bureau of IUTAM, includes the following members: F. L. Chernousko, Moscow, Russia E. Kreuzer, Hamburg, Germany (Co-Chairman) H. Y. Hu, Nanjing, China (Chairman) A. H. Nayfeh, Blacksburg, USA G. Rega, Rome, Italy W. Schiehlen, Stuttgart, Germany (IUTAM representative) K. Sobczyk, Warsaw, Poland G. Stepan, Budapest, Hungary H. Troger, Wien, Austria ix x Preface