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Preface
6
Contents
Contents
Contributors
12
Part I Nonlinear and Discontinuous Dynamical Systems
18
1 General Solution of a Vibration System with Damping Force of Fractional-Order Derivative
19
1.1 Introduction
19
1.2 Preliminaries for Sequential Fractional-Order Differential Equations
20
1.2.1 Linear Dependence and Linear Independence of Functions
21
1.2.2 Characteristic Polynomial
21
1.2.3 General Solution of SFDE
23
1.3 Analysis of the Characteristic Roots
23
1.4 The General Solution
25
References
27
2 An Analytic Proof for the Sensitivity of Chaos to Initial Condition and Perturbations
28
2.1 Introduction
28
2.2 Perturbation Equations
29
2.3 General Solutions of Perturbation Equations
30
2.4 Sensitivity to the Initial Conditions
34
2.5 Sensitivity to Perturbations
35
References
36
3 Study on the Multifractal Spectrum of Local Area Networks Traffic and Their Correlations
37
3.1 Introduction
37
3.2 Multifractal and the Spectral Parameters for Networks Traffic
38
3.3 Relationship Between Variables of Multifractal Spectrum
39
3.4 Numerical Simulation and Analysis
40
3.4.1 Multifractal Spectrum and Parameters
40
3.4.2 Relationship Between Multifractal Spectrum Parameters and Traffic Variation
42
3.5 Concluding Remarks
43
References
44
4 A Boundary Crisis in High Dimensional Chaotic Systems
45
4.1 Introduction
45
4.2 A Hyperchaotic Boundary Crisis in a Kawakami Map
46
4.3 Concluding Remarks
49
References
50
5 Complete Bifurcation Behaviors of a Henon Map
51
5.1 Introduction
51
5.2 Analysis
52
5.3 Illustrations
54
5.4 Conclusion
60
References
61
6 Study on the Performance of a Two-Degree-of-Freedom Chaotic Vibration Isolation System
62
6.1 Introduction
62
6.2 Model of the Two-Degree-of-Freedom Nonlinear Vibration Isolation System
63
6.3 Dynamical Analysis
65
6.4 Analysis of the Power Flow
69
6.5 Conclusion
70
References
73
7 Simulation and Nonlinear Analysis of Panel Flutter with Thermal Effects in Supersonic Flow
74
7.1 Introduction
74
7.2 Governing Equation
75
7.2.1 Dynamic Loads and Heating
76
7.2.2 Solution of Heat Transfer
76
7.2.3 Governing Equations
77
7.2.4 Galerkin Method
78
7.3 Numerical Results
80
7.3.1 Rf =0, Mach Number as the Bifurcation Parameter
80
7.3.2 Rf =0.056, Mach Number as the Bifurcation Parameter
82
7.3.3 M=2, Rf as Bifurcation Parameter
85
7.4 Conclusions
87
References
89
8 A Parameter Study of a Machine Tool with Multiple Boundaries
90
8.1 Introduction
90
8.2 Structured Motions by the Mapping Technique
91
8.3 Domains and Boundaries
94
8.4 Motion Switch Ability Conditions
95
8.5 Parameter Study of (e, )
96
8.6 Numerical Prediction of Eccentricity Frequency
100
8.7 Summary and Conclusions
103
References
106
9 A New Friction Model for Evaluating Energy Dissipation in Carbon Nanotube-Based Composites
108
9.1 Introduction
108
9.2 Vibration Model
110
9.3 Results and Discussion
112
9.3.1 Excitation Frequency and Binding Strength
113
9.3.2 Excitation's Amplitude
114
9.3.3 Compliance Number M
114
9.4 Summary
116
References
116
10 Nonlinear Response in a Rotor System With a Coulomb Spline
118
10.1 Introduction
118
10.2 Mathematical Modeling
119
10.3 Analysis
121
10.4 Conclusion
133
References
133
11 The Influence of the Cross-Coupling Effects on the Dynamics of Rotor/Stator Rubbing
134
11.1 Introduction
134
11.2 The Rotor/Stator Model with Cross-Coupling Effects
135
11.3 The Solution and the Stability Analysis
136
11.3.1 Synchronous Full Annular Rub Solution
137
11.3.2 Stability Analysis
138
11.4 The Cross-Coupling Effects on the Stability
140
11.4.1 Stability Domains in the Plane of -
141
11.4.2 Stability Domains in the Plane of -sr
142
11.4.3 Stability Domains in the Plane of -Msr
143
11.5 Conclusions
144
References
145
Part II Time-delay Systems
146
12 Some Control Studies of Dynamical Systems with Time Delay
147
12.1 Introduction
147
12.2 Methods of Solution
149
12.2.1 Semi-Discretization
149
12.2.2 Continuous Time Approximation
151
12.3 Spectral Properties of the Methods
152
12.4 Control Formulations
155
12.4.1 Full-State Feedback Optimal Control
155
12.4.2 Output Feedback Optimal Control
155
12.4.3 Optimal Feedback Gains via Mapping
156
12.5 Supervisory Control
157
12.6 Numerical Examples
158
12.6.1 Linear Time Invariant System
158
12.6.2 Periodic System
159
12.6.3 An Experimental Example
164
12.7 Concluding Remarks
166
References
166
13 Stability and Hopf Bifurcation Analysis in Synaptically Coupled FHN Neurons with Two Time Delays
168
13.1 Introduction
168
13.2 Stability Analysis
170
13.3 The Direction and Stability of Hopf Bifurcation
174
References
177
14 On the Feedback Controlling of the Neuronal Systemwith Time Delay
179
14.1 Introduction
179
14.2 HR Model Neuron with Time Delay
180
14.3 Influence of Synaptic Intensity on the Neuronal Discharge
181
14.4 Influence of Time Delay on the Neuronal Discharge
182
14.5 Controlling Chaotic Discharge by Feedback Control with Time Delay
182
14.6 Conclusions
183
References
184
15 Control of Erosion of Safe Basins in a Single Degree of Freedom Yaw System of a Ship with a Delayed Position Feedback
186
15.1 Introduction
186
15.2 Effects of the Time Delay on the Basin Boundary
187
15.3 Effects of the Delay on the Area of the Safe Basin
191
15.4 Conclusions
193
References
193
Part III Switching and Stochastic Dynamical Systems
195
16 On Periodic Flows of a 3-D Switching System with Many Subsystems
196
16.1 Introduction
196
16.2 Methodology for Periodic Flows
198
16.3 Analytical Predictions
203
16.4 Numerical Illustrations
207
16.5 Conclusions
207
References
207
17 Impulsive Control Induced Effects on Dynamicsof Complex Networks
209
17.1 Introduction
209
17.2 Main Results
210
17.2.1 Stability Analysis of the Presented Dynamical Networks with Different Dynamical Nodes with Impulsive Control
211
17.2.2 Impulsive Control Induced Effects on Dynamics of Complex Networks with Identical Dynamical Nodes
212
17.3 Numerical Simulations
217
17.4 Conclusion
221
References
221
18 Study on Synchronization of Two Identical Uncoupled Neurons Induced by Noise
223
18.1 Introduction
223
18.2 Numerical Results and Discussion
224
18.3 Conclusions
227
References
227
19 Non-equilibrium Phase Transitions in a Single-Mode Laser Model Driven by Non-Gaussian Noise
228
19.1 Introduction
228
19.2 Approximate Stationary Probability Distribution
230
19.3 General Analysis
232
19.4 Conclusion Remarks
234
References
235
20 Dynamical Properties of Intensity Fluctuation of Saturation Laser Model Driven by Cross-Correlated Additive and Multiplicative Noises
237
20.1 Introduction
237
20.2 Stationary Probability Distribution and Relaxation Time and Correlated Function
239
20.3 Discussion and Conclusion
244
References
252
21 Empirical Mode Decomposition Based on Bistable Stochastic Resonance Denoising
254
21.1 Introduction
254
21.2 Empirical Mode Decomposition
255
21.2.1 IMFs
255
21.2.2 The Sifting Processing
255
21.2.3 Examples
256
21.3 Stochastive Resonance
257
21.3.1 Bistable System
258
21.3.2 Examples
259
21.4 Test of EMD Based on SR Denoising
260
21.5 Conclusion
261
References
262
Part IV Classic Vibrations and Control
263
22 Order Reduction of a Two-Span Rotor-Bearing System Via the Predictor-Corrector Galerkin Method
264
22.1 Introduction
264
22.2 Modeling of the Two-Span Rotor-Bearing System
266
22.3 The Predictor-Corrector Galerkin Method
267
22.4 Numerical Results and Discussion
269
22.5 Conclusions
273
References
273
23 Stiffness Nonlinearity Classification Using Morlet Wavelets
275
23.1 Introduction
275
23.2 Response of the Nonlinear System
276
23.3 Wavelet Transform
278
23.3.1 Wavelet Transform of the Response Signal
278
23.3.1.1 Standard Morlet Wavelet
279
23.3.1.2 Complete Morlet Wavelet
280
23.4 Illustration
281
23.5 Conclusions
283
References
284
24 Dynamics of Wire-Driven Machine Mechanisms: Literature Review
285
24.1 Introduction
285
24.2 Mechanical Properties of Wire Ropes
287
24.2.1 Young's Modulus
287
24.2.2 Damping
289
24.3 Dynamics Simulation of Wire Rope Systems
291
24.3.1 Belt–Pulley Systems
292
24.3.2 Complex Wire Rope Systems
293
24.4 Conclusions
297
References
297
25 Dynamics of Wire-Driven Machine Mechanisms, Part II: Theory and Applications
299
25.1 Introduction
299
25.2 Wire Mechanics
301
25.2.1 Wire Topology
301
25.2.2 Elastic Properties of Wire and Chain Elements
302
25.2.3 Kinematics of Wire Motion
304
25.2.4 Tension Dynamics
306
25.3 Boom Mechanics
307
25.4 Fluid Power Circuit
308
25.5 System Dynamics Examples
310
25.5.1 Hydraulic Winch System
311
25.5.2 Chain Driven Elevating Boom
313
25.6 Conclusion
316
References
317
26 On Analytical Methods for Vibrations of Soils and Foundations
318
26.1 Introduction
318
26.2 Surface Response Due to Concentrated Forces
319
26.3 Dynamic Response of Foundations
321
26.3.1 Assumed Contact Stress Distributions
321
26.3.2 Mixed Boundary Value Problems
322
26.3.3 Lumped Parameter Models
329
26.3.4 Computational Methods
330
26.4 Coupled Vibrations of Foundations
331
26.5 Interactions Between Foundations
332
26.6 Experimental Studies
333
26.7 Conclusions
334
References
334
27 Inversely Found Elastic and Dimensional Properties
340
27.1 Introduction
340
27.2 Computational Overview
341
27.3 Simplifying Features
346
27.4 Graphical Relations Between the Cut-Off Frequencies and Cylinder Properties
347
27.5 Inversion Scheme
350
27.6 Illustrative Examples
351
27.6.1 Numerical Simulation
351
27.6.2 Experimental Corroboration
352
27.7 Conclusions
352
References
353
28 Nonlinear Self-Defined Truss Element Based on the Plane Truss Structure with Flexible Connector
355
28.1 Introduction
355
28.2 Finite-Element Dynamic Modeling
357
28.2.1 Introduction of the Structure
357
28.2.2 Motion Equations of the Self-Defined Truss Element
358
28.3 Nonlinear Nodal Forces
359
28.4 The Numerical Solution Method and Example
360
28.4.1 The Numerical Solution Method
360
28.4.2 Numerical Example
360
28.4.2.1 Random Excitation
361
28.4.2.2 Contact Stiffness
363
28.4.2.3 Clearance
365
28.5 Conclusions
367
References
368
29 Complex Frequency Analysis of an Axially Moving String with Multiple Attached Oscillators by Using Green's Function Method
369
29.1 Introduction
369
29.2 Formulation of the Eigenvalue Problem
370
29.3 Construction of Green's Function
372
29.4 Results and Discussions
373
29.5 Conclusion
378
References
379
30 Model Reduction on Inertial Manifolds of Navier–Stokes Equations Through Multi-scale Finite Element
380
30.1 Introduction
380
30.2 Multilevel Finite Element Method
383
30.3 The Weak Form of the Navier–Stokes Equations
385
30.4 Numerical Methods
386
30.5 Large Eddy and Small Eddy Components
387
30.6 Numerical Examples
389
30.7 Concluding Remarks
391
References
392
31 Diesel Engine Condition Classification Based on Mechanical Dynamics and Time-Frequency Image Processing
394
31.1 Introduction
394
31.2 Diesel Engine Structure Dynamics
395
31.3 Classification by Time Frequency Image
398
31.3.1 Hilbert Time-Frequency Spectrum
398
31.3.2 Euclidean Distance
399
31.3.3 Condition Classification
400
31.4 Example Analysis
400
31.4.1 Experiment
400
31.4.2 Vibration Signal Analysis
401
31.4.3 Hilbert Spectrum Recognition
401
31.4.4 ED Discriminant
403
31.5 Conclusions
405
References
405
32 Input Design for Systems Under Identification as Applied to Ultrasonic Transducers
406
32.1 Introduction
406
32.2 Input Design Formulation for ARX Models
407
32.3 System Identification Algorithm
410
32.4 Input Design for System Identification
412
32.5 Experimental Results
413
32.6 Conclusions and Recommendations
416
References
417
33 Development of a Control System for Automating of SpiralConcentrators in Coal Preparation Plants
418
33.1 Introduction
418
33.2 Technical Approach
421
33.2.1 Metal Arms and Wheatstone Bridge
422
33.2.2 Differential Amplifiers
423
33.2.3 PIC Microcontroller and Motor
423
33.2.4 Demonstration
424
33.2.5 Assembly
425
33.3 Mechanical System Design
425
33.4 The Need for a Model
428
33.5 Conclusions
431
References
432
34 On the Rough Number Computation and the Ada Language
433
34.1 Introduction
433
34.2 Some Basic Algebraic Structures
434
34.3 The Structure of Dyadic Numbers
436
34.4 The Structure of Rough Numbers
437
34.5 Hierarchical Classes and Computation
438
34.6 The Ada Language and Rough Number Computation
440
34.7 Conclusions
442
References
443
Author Index
444
Subject Index
455
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