Luo Dynamical Systems

Discontinuity, Stochasticity and Time-Delay
1. Auflage 2010
ISBN: 978-1-4419-5754-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 464 Seiten

Dynamical Systems: Discontinuous, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuses on the most recent advances in all three areas, with particular emphasis on recent analytical, numerical and experimental research and its results. Real dynamical system problems, such as the behavior of suspension systems of railways, nonlinear vibration and applied control in coal manufacturing, along with the multifractal spectrum of LAN traffic, are discussed at length, giving the reader a sense of real-world instances where these theories are applied. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay also contains material on time-delay systems as they relate to linear switching, dynamics of complex networks, and machine tools with multiple boundaries. It is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.

Autoren/Hrsg.

Luo, Albert C. J.

Inhaltsverzeichnis

1;Preface;6
2;Contents
;8
3;Contributors;12
4;Part I Nonlinear and Discontinuous Dynamical Systems;18
4.1;1 General Solution of a Vibration System with Damping Force of Fractional-Order Derivative;19
4.1.1;1.1 Introduction;19
4.1.2;1.2 Preliminaries for Sequential Fractional-Order Differential Equations;20
4.1.2.1;1.2.1 Linear Dependence and Linear Independence of Functions;21
4.1.2.2;1.2.2 Characteristic Polynomial;21
4.1.2.3;1.2.3 General Solution of SFDE;23
4.1.3;1.3 Analysis of the Characteristic Roots;23
4.1.4;1.4 The General Solution;25
4.1.5;References;27
4.2;2 An Analytic Proof for the Sensitivity of Chaos to Initial Condition and Perturbations;28
4.2.1;2.1 Introduction;28
4.2.2;2.2 Perturbation Equations;29
4.2.3;2.3 General Solutions of Perturbation Equations;30
4.2.4;2.4 Sensitivity to the Initial Conditions;34
4.2.5;2.5 Sensitivity to Perturbations;35
4.2.6;References;36
4.3;3 Study on the Multifractal Spectrum of Local Area Networks Traffic and Their Correlations;37
4.3.1;3.1 Introduction;37
4.3.2;3.2 Multifractal and the Spectral Parameters for Networks Traffic;38
4.3.3;3.3 Relationship Between Variables of Multifractal Spectrum;39
4.3.4;3.4 Numerical Simulation and Analysis;40
4.3.4.1;3.4.1 Multifractal Spectrum and Parameters;40
4.3.4.2;3.4.2 Relationship Between Multifractal Spectrum Parameters and Traffic Variation;42
4.3.5;3.5 Concluding Remarks;43
4.3.6;References;44
4.4;4 A Boundary Crisis in High Dimensional Chaotic Systems;45
4.4.1;4.1 Introduction;45
4.4.2;4.2 A Hyperchaotic Boundary Crisis in a Kawakami Map ;46
4.4.3;4.3 Concluding Remarks;49
4.4.4;References;50
4.5;5 Complete Bifurcation Behaviors of a Henon Map;51
4.5.1;5.1 Introduction;51
4.5.2;5.2 Analysis;52
4.5.3;5.3 Illustrations;54
4.5.4;5.4 Conclusion;60
4.5.5;References;61
4.6;6 Study on the Performance of a Two-Degree-of-Freedom Chaotic Vibration Isolation System;62
4.6.1;6.1 Introduction;62
4.6.2;6.2 Model of the Two-Degree-of-Freedom Nonlinear Vibration Isolation System;63
4.6.3;6.3 Dynamical Analysis;65
4.6.4;6.4 Analysis of the Power Flow;69
4.6.5;6.5 Conclusion;70
4.6.6;References;73
4.7;7 Simulation and Nonlinear Analysis of Panel Flutter with Thermal Effects in Supersonic Flow;74
4.7.1;7.1 Introduction;74
4.7.2;7.2 Governing Equation;75
4.7.2.1;7.2.1 Dynamic Loads and Heating;76
4.7.2.2;7.2.2 Solution of Heat Transfer;76
4.7.2.3;7.2.3 Governing Equations;77
4.7.2.4;7.2.4 Galerkin Method;78
4.7.3;7.3 Numerical Results;80
4.7.3.1;7.3.1 Rf =0, Mach Number as the Bifurcation Parameter;80
4.7.3.2;7.3.2 Rf =0.056, Mach Number as the Bifurcation Parameter;82
4.7.3.3;7.3.3 M=2, Rf as Bifurcation Parameter;85
4.7.4;7.4 Conclusions;87
4.7.5;References;89
4.8;8 A Parameter Study of a Machine Tool with Multiple Boundaries;90
4.8.1;8.1 Introduction;90
4.8.2;8.2 Structured Motions by the Mapping Technique;91
4.8.3;8.3 Domains and Boundaries;94
4.8.4;8.4 Motion Switch Ability Conditions;95
4.8.5;8.5 Parameter Study of (e, );96
4.8.6;8.6 Numerical Prediction of Eccentricity Frequency ;100
4.8.7;8.7 Summary and Conclusions;103
4.8.8;References;106
4.9;9 A New Friction Model for Evaluating Energy Dissipation in Carbon Nanotube-Based Composites;108
4.9.1;9.1 Introduction;108
4.9.2;9.2 Vibration Model;110
4.9.3;9.3 Results and Discussion;112
4.9.3.1;9.3.1 Excitation Frequency and Binding Strength;113
4.9.3.2;9.3.2 Excitation's Amplitude;114
4.9.3.3;9.3.3 Compliance Number M;114
4.9.4;9.4 Summary;116
4.9.5;References;116
4.10;10 Nonlinear Response in a Rotor System With a Coulomb Spline;118
4.10.1;10.1 Introduction;118
4.10.2;10.2 Mathematical Modeling;119
4.10.3;10.3 Analysis;121
4.10.4;10.4 Conclusion;133
4.10.5;References;133
4.11;11 The Influence of the Cross-Coupling Effects on the Dynamics of Rotor/Stator Rubbing;134
4.11.1;11.1 Introduction;134
4.11.2;11.2 The Rotor/Stator Model with Cross-Coupling Effects;135
4.11.3;11.3 The Solution and the Stability Analysis;136
4.11.3.1;11.3.1 Synchronous Full Annular Rub Solution;137
4.11.3.2;11.3.2 Stability Analysis;138
4.11.4;11.4 The Cross-Coupling Effects on the Stability;140
4.11.4.1;11.4.1 Stability Domains in the Plane of -;141
4.11.4.2;11.4.2 Stability Domains in the Plane of -sr;142
4.11.4.3;11.4.3 Stability Domains in the Plane of -Msr;143
4.11.5;11.5 Conclusions;144
4.11.6;References;145
5;Part II Time-delay Systems;146
5.1;12 Some Control Studies of Dynamical Systems with Time Delay;147
5.1.1;12.1 Introduction;147
5.1.2;12.2 Methods of Solution;149
5.1.2.1;12.2.1 Semi-Discretization;149
5.1.2.2;12.2.2 Continuous Time Approximation;151
5.1.3;12.3 Spectral Properties of the Methods ;152
5.1.4;12.4 Control Formulations;155
5.1.4.1;12.4.1 Full-State Feedback Optimal Control;155
5.1.4.2;12.4.2 Output Feedback Optimal Control;155
5.1.4.3;12.4.3 Optimal Feedback Gains via Mapping;156
5.1.5;12.5 Supervisory Control;157
5.1.6;12.6 Numerical Examples;158
5.1.6.1;12.6.1 Linear Time Invariant System;158
5.1.6.2;12.6.2 Periodic System;159
5.1.6.3;12.6.3 An Experimental Example;164
5.1.7;12.7 Concluding Remarks;166
5.1.8;References;166
5.2;13 Stability and Hopf Bifurcation Analysis in Synaptically Coupled FHN Neurons with Two Time Delays;168
5.2.1;13.1 Introduction;168
5.2.2;13.2 Stability Analysis;170
5.2.3;13.3 The Direction and Stability of Hopf Bifurcation;174
5.2.4;References;177
5.3;14 On the Feedback Controlling of the Neuronal Systemwith Time Delay;179
5.3.1;14.1 Introduction;179
5.3.2;14.2 HR Model Neuron with Time Delay;180
5.3.3;14.3 Influence of Synaptic Intensity on the Neuronal Discharge;181
5.3.4;14.4 Influence of Time Delay on the Neuronal Discharge;182
5.3.5;14.5 Controlling Chaotic Discharge by Feedback Control with Time Delay;182
5.3.6;14.6 Conclusions;183
5.3.7;References;184
5.4;15 Control of Erosion of Safe Basins in a Single Degree of Freedom Yaw System of a Ship with a Delayed Position Feedback;186
5.4.1;15.1 Introduction;186
5.4.2;15.2 Effects of the Time Delay on the Basin Boundary;187
5.4.3;15.3 Effects of the Delay on the Area of the Safe Basin;191
5.4.4;15.4 Conclusions;193
5.4.5;References;193
6;Part III Switching and Stochastic Dynamical Systems;195
6.1;16 On Periodic Flows of a 3-D Switching System with Many Subsystems;196
6.1.1;16.1 Introduction;196
6.1.2;16.2 Methodology for Periodic Flows;198
6.1.3;16.3 Analytical Predictions;203
6.1.4;16.4 Numerical Illustrations;207
6.1.5;16.5 Conclusions;207
6.1.6;References;207
6.2;17 Impulsive Control Induced Effects on Dynamicsof Complex Networks;209
6.2.1;17.1 Introduction;209
6.2.2;17.2 Main Results;210
6.2.2.1;17.2.1 Stability Analysis of the Presented Dynamical Networks with Different Dynamical Nodes with Impulsive Control;211
6.2.2.2;17.2.2 Impulsive Control Induced Effects on Dynamics of Complex Networks with Identical Dynamical Nodes;212
6.2.3;17.3 Numerical Simulations;217
6.2.4;17.4 Conclusion;221
6.2.5;References;221
6.3;18 Study on Synchronization of Two Identical Uncoupled Neurons Induced by Noise;223
6.3.1;18.1 Introduction;223
6.3.2;18.2 Numerical Results and Discussion;224
6.3.3;18.3 Conclusions;227
6.3.4;References;227
6.4;19 Non-equilibrium Phase Transitions in a Single-Mode Laser Model Driven by Non-Gaussian Noise;228
6.4.1;19.1 Introduction;228
6.4.2;19.2 Approximate Stationary Probability Distribution;230
6.4.3;19.3 General Analysis;232
6.4.4;19.4 Conclusion Remarks;234
6.4.5;References;235
6.5;20 Dynamical Properties of Intensity Fluctuation of Saturation Laser Model Driven by Cross-Correlated Additive and Multiplicative Noises;237
6.5.1;20.1 Introduction;237
6.5.2;20.2 Stationary Probability Distribution and Relaxation Time and Correlated Function;239
6.5.3;20.3 Discussion and Conclusion;244
6.5.4;References;252
6.6;21 Empirical Mode Decomposition Based on Bistable Stochastic Resonance Denoising;254
6.6.1;21.1 Introduction;254
6.6.2;21.2 Empirical Mode Decomposition;255
6.6.2.1;21.2.1 IMFs;255
6.6.2.2;21.2.2 The Sifting Processing;255
6.6.2.3;21.2.3 Examples;256
6.6.3;21.3 Stochastive Resonance;257
6.6.3.1;21.3.1 Bistable System;258
6.6.3.2;21.3.2 Examples;259
6.6.4;21.4 Test of EMD Based on SR Denoising;260
6.6.5;21.5 Conclusion;261
6.6.6;References;262
7;Part IV Classic Vibrations and Control;263
7.1;22 Order Reduction of a Two-Span Rotor-Bearing System Via the Predictor-Corrector Galerkin Method;264
7.1.1;22.1 Introduction;264
7.1.2;22.2 Modeling of the Two-Span Rotor-Bearing System;266
7.1.3;22.3 The Predictor-Corrector Galerkin Method;267
7.1.4;22.4 Numerical Results and Discussion;269
7.1.5;22.5 Conclusions;273
7.1.6;References;273
7.2;23 Stiffness Nonlinearity Classification Using Morlet Wavelets;275
7.2.1;23.1 Introduction;275
7.2.2;23.2 Response of the Nonlinear System;276
7.2.3;23.3 Wavelet Transform;278
7.2.3.1;23.3.1 Wavelet Transform of the Response Signal;278
7.2.3.1.1;23.3.1.1 Standard Morlet Wavelet;279
7.2.3.1.2;23.3.1.2 Complete Morlet Wavelet;280
7.2.4;23.4 Illustration;281
7.2.5;23.5 Conclusions;283
7.2.6;References;284
7.3;24 Dynamics of Wire-Driven Machine Mechanisms: Literature Review;285
7.3.1;24.1 Introduction;285
7.3.2;24.2 Mechanical Properties of Wire Ropes;287
7.3.2.1;24.2.1 Young's Modulus;287
7.3.2.2;24.2.2 Damping;289
7.3.3;24.3 Dynamics Simulation of Wire Rope Systems;291
7.3.3.1;24.3.1 Belt–Pulley Systems;292
7.3.3.2;24.3.2 Complex Wire Rope Systems;293
7.3.4;24.4 Conclusions;297
7.3.5;References;297
7.4;25 Dynamics of Wire-Driven Machine Mechanisms, Part II: Theory and Applications;299
7.4.1;25.1 Introduction;299
7.4.2;25.2 Wire Mechanics;301
7.4.2.1;25.2.1 Wire Topology;301
7.4.2.2;25.2.2 Elastic Properties of Wire and Chain Elements;302
7.4.2.3;25.2.3 Kinematics of Wire Motion;304
7.4.2.4;25.2.4 Tension Dynamics;306
7.4.3;25.3 Boom Mechanics;307
7.4.4;25.4 Fluid Power Circuit;308
7.4.5;25.5 System Dynamics Examples;310
7.4.5.1;25.5.1 Hydraulic Winch System;311
7.4.5.2;25.5.2 Chain Driven Elevating Boom;313
7.4.6;25.6 Conclusion;316
7.4.7;References;317
7.5;26 On Analytical Methods for Vibrations of Soils and Foundations;318
7.5.1;26.1 Introduction;318
7.5.2;26.2 Surface Response Due to Concentrated Forces;319
7.5.3;26.3 Dynamic Response of Foundations;321
7.5.3.1;26.3.1 Assumed Contact Stress Distributions;321
7.5.3.2;26.3.2 Mixed Boundary Value Problems;322
7.5.3.3;26.3.3 Lumped Parameter Models;329
7.5.3.4;26.3.4 Computational Methods;330
7.5.4;26.4 Coupled Vibrations of Foundations;331
7.5.5;26.5 Interactions Between Foundations;332
7.5.6;26.6 Experimental Studies;333
7.5.7;26.7 Conclusions;334
7.5.8;References;334
7.6;27 Inversely Found Elastic and Dimensional Properties;340
7.6.1;27.1 Introduction;340
7.6.2;27.2 Computational Overview;341
7.6.3;27.3 Simplifying Features;346
7.6.4;27.4 Graphical Relations Between the Cut-Off Frequencies and Cylinder Properties;347
7.6.5;27.5 Inversion Scheme;350
7.6.6;27.6 Illustrative Examples;351
7.6.6.1;27.6.1 Numerical Simulation;351
7.6.6.2;27.6.2 Experimental Corroboration;352
7.6.7;27.7 Conclusions;352
7.6.8;References;353
7.7;28 Nonlinear Self-Defined Truss Element Based on the Plane Truss Structure with Flexible Connector;355
7.7.1;28.1 Introduction;355
7.7.2;28.2 Finite-Element Dynamic Modeling;357
7.7.2.1;28.2.1 Introduction of the Structure;357
7.7.2.2;28.2.2 Motion Equations of the Self-Defined Truss Element;358
7.7.3;28.3 Nonlinear Nodal Forces;359
7.7.4;28.4 The Numerical Solution Method and Example;360
7.7.4.1;28.4.1 The Numerical Solution Method;360
7.7.4.2;28.4.2 Numerical Example;360
7.7.4.2.1;28.4.2.1 Random Excitation;361
7.7.4.2.2;28.4.2.2 Contact Stiffness;363
7.7.4.2.3;28.4.2.3 Clearance;365
7.7.5;28.5 Conclusions;367
7.7.6;References;368
7.8;29 Complex Frequency Analysis of an Axially Moving String with Multiple Attached Oscillators by Using Green's Function Method;369
7.8.1;29.1 Introduction;369
7.8.2;29.2 Formulation of the Eigenvalue Problem;370
7.8.3;29.3 Construction of Green's Function;372
7.8.4;29.4 Results and Discussions;373
7.8.5;29.5 Conclusion;378
7.8.6;References;379
7.9;30 Model Reduction on Inertial Manifolds of Navier–Stokes Equations Through Multi-scale Finite Element;380
7.9.1;30.1 Introduction;380
7.9.2;30.2 Multilevel Finite Element Method;383
7.9.3;30.3 The Weak Form of the Navier–Stokes Equations;385
7.9.4;30.4 Numerical Methods;386
7.9.5;30.5 Large Eddy and Small Eddy Components;387
7.9.6;30.6 Numerical Examples;389
7.9.7;30.7 Concluding Remarks;391
7.9.8;References;392
7.10;31 Diesel Engine Condition Classification Based on Mechanical Dynamics and Time-Frequency Image Processing;394
7.10.1;31.1 Introduction;394
7.10.2;31.2 Diesel Engine Structure Dynamics;395
7.10.3;31.3 Classification by Time Frequency Image;398
7.10.3.1;31.3.1 Hilbert Time-Frequency Spectrum;398
7.10.3.2;31.3.2 Euclidean Distance;399
7.10.3.3;31.3.3 Condition Classification;400
7.10.4;31.4 Example Analysis;400
7.10.4.1;31.4.1 Experiment;400
7.10.4.2;31.4.2 Vibration Signal Analysis;401
7.10.4.3;31.4.3 Hilbert Spectrum Recognition;401
7.10.4.4;31.4.4 ED Discriminant;403
7.10.5;31.5 Conclusions;405
7.10.6;References;405
7.11;32 Input Design for Systems Under Identification as Applied to Ultrasonic Transducers;406
7.11.1;32.1 Introduction;406
7.11.2;32.2 Input Design Formulation for ARX Models;407
7.11.3;32.3 System Identification Algorithm;410
7.11.4;32.4 Input Design for System Identification;412
7.11.5;32.5 Experimental Results;413
7.11.6;32.6 Conclusions and Recommendations;416
7.11.7;References;417
7.12;33 Development of a Control System for Automating of SpiralConcentrators in Coal Preparation Plants;418
7.12.1;33.1 Introduction;418
7.12.2;33.2 Technical Approach;421
7.12.2.1;33.2.1 Metal Arms and Wheatstone Bridge;422
7.12.2.2;33.2.2 Differential Amplifiers;423
7.12.2.3;33.2.3 PIC Microcontroller and Motor;423
7.12.2.4;33.2.4 Demonstration;424
7.12.2.5;33.2.5 Assembly;425
7.12.3;33.3 Mechanical System Design;425
7.12.4;33.4 The Need for a Model;428
7.12.5;33.5 Conclusions;431
7.12.6;References;432
7.13;34 On the Rough Number Computation and the Ada Language;433
7.13.1;34.1 Introduction;433
7.13.2;34.2 Some Basic Algebraic Structures;434
7.13.3;34.3 The Structure of Dyadic Numbers;436
7.13.4;34.4 The Structure of Rough Numbers;437
7.13.5;34.5 Hierarchical Classes and Computation;438
7.13.6;34.6 The Ada Language and Rough Number Computation;440
7.13.7;34.7 Conclusions;442
7.13.8;References;443
8;Author Index;444
9;Subject Index;455