Dynamical Systems - Discontinuity, Stochasticity and Time-Delay

Preface

Contents

Contributors

Part I Nonlinear and Discontinuous Dynamical Systems

1 General Solution of a Vibration System with Damping Force of Fractional-Order Derivative

1.1 Introduction

1.2 Preliminaries for Sequential Fractional-Order Differential Equations

1.2.1 Linear Dependence and Linear Independence of Functions

1.2.2 Characteristic Polynomial

1.2.3 General Solution of SFDE

1.3 Analysis of the Characteristic Roots

1.4 The General Solution

References

2 An Analytic Proof for the Sensitivity of Chaos to Initial Condition and Perturbations

2.1 Introduction

2.2 Perturbation Equations

2.3 General Solutions of Perturbation Equations

2.4 Sensitivity to the Initial Conditions

2.5 Sensitivity to Perturbations

References

3 Study on the Multifractal Spectrum of Local Area Networks Traffic and Their Correlations

3.1 Introduction

3.2 Multifractal and the Spectral Parameters for Networks Traffic

3.3 Relationship Between Variables of Multifractal Spectrum

3.4 Numerical Simulation and Analysis

3.4.1 Multifractal Spectrum and Parameters

3.4.2 Relationship Between Multifractal Spectrum Parameters and Traffic Variation

3.5 Concluding Remarks

References

4 A Boundary Crisis in High Dimensional Chaotic Systems

4.1 Introduction

4.2 A Hyperchaotic Boundary Crisis in a Kawakami Map

4.3 Concluding Remarks

References

5 Complete Bifurcation Behaviors of a Henon Map

5.1 Introduction

5.2 Analysis

5.3 Illustrations

5.4 Conclusion

References

6 Study on the Performance of a Two-Degree-of-Freedom Chaotic Vibration Isolation System

6.1 Introduction

6.2 Model of the Two-Degree-of-Freedom Nonlinear Vibration Isolation System

6.3 Dynamical Analysis

6.4 Analysis of the Power Flow

6.5 Conclusion

References

7 Simulation and Nonlinear Analysis of Panel Flutter with Thermal Effects in Supersonic Flow

7.1 Introduction

7.2 Governing Equation

7.2.1 Dynamic Loads and Heating

7.2.2 Solution of Heat Transfer

7.2.3 Governing Equations

7.2.4 Galerkin Method

7.3 Numerical Results

7.3.1 Rf =0, Mach Number as the Bifurcation Parameter

7.3.2 Rf =0.056, Mach Number as the Bifurcation Parameter

7.3.3 M=2, Rf as Bifurcation Parameter

7.4 Conclusions

References

8 A Parameter Study of a Machine Tool with Multiple Boundaries

8.1 Introduction

8.2 Structured Motions by the Mapping Technique

8.3 Domains and Boundaries

8.4 Motion Switch Ability Conditions

8.5 Parameter Study of (e, )

8.6 Numerical Prediction of Eccentricity Frequency

8.7 Summary and Conclusions

References

9 A New Friction Model for Evaluating Energy Dissipation in Carbon Nanotube-Based Composites

9.1 Introduction

9.2 Vibration Model

9.3 Results and Discussion

9.3.1 Excitation Frequency and Binding Strength

9.3.2 Excitation's Amplitude

9.3.3 Compliance Number M

9.4 Summary

References

10 Nonlinear Response in a Rotor System With a Coulomb Spline

10.1 Introduction

10.2 Mathematical Modeling

10.3 Analysis

10.4 Conclusion

References

11 The Influence of the Cross-Coupling Effects on the Dynamics of Rotor/Stator Rubbing

11.1 Introduction

11.2 The Rotor/Stator Model with Cross-Coupling Effects

11.3 The Solution and the Stability Analysis

11.3.1 Synchronous Full Annular Rub Solution

11.3.2 Stability Analysis

11.4 The Cross-Coupling Effects on the Stability

11.4.1 Stability Domains in the Plane of -

11.4.2 Stability Domains in the Plane of -sr

11.4.3 Stability Domains in the Plane of -Msr

11.5 Conclusions

References

Part II Time-delay Systems

12 Some Control Studies of Dynamical Systems with Time Delay

12.1 Introduction

12.2 Methods of Solution

12.2.1 Semi-Discretization

12.2.2 Continuous Time Approximation

12.3 Spectral Properties of the Methods

12.4 Control Formulations

12.4.1 Full-State Feedback Optimal Control

12.4.2 Output Feedback Optimal Control

12.4.3 Optimal Feedback Gains via Mapping

12.5 Supervisory Control

12.6 Numerical Examples

12.6.1 Linear Time Invariant System

12.6.2 Periodic System

12.6.3 An Experimental Example

12.7 Concluding Remarks

References

13 Stability and Hopf Bifurcation Analysis in Synaptically Coupled FHN Neurons with Two Time Delays

13.1 Introduction

13.2 Stability Analysis

13.3 The Direction and Stability of Hopf Bifurcation

References

14 On the Feedback Controlling of the Neuronal Systemwith Time Delay

14.1 Introduction

14.2 HR Model Neuron with Time Delay

14.3 Influence of Synaptic Intensity on the Neuronal Discharge

14.4 Influence of Time Delay on the Neuronal Discharge

14.5 Controlling Chaotic Discharge by Feedback Control with Time Delay

14.6 Conclusions

References

15 Control of Erosion of Safe Basins in a Single Degree of Freedom Yaw System of a Ship with a Delayed Position Feedback

15.1 Introduction

15.2 Effects of the Time Delay on the Basin Boundary

15.3 Effects of the Delay on the Area of the Safe Basin

15.4 Conclusions

References

Part III Switching and Stochastic Dynamical Systems

16 On Periodic Flows of a 3-D Switching System with Many Subsystems

16.1 Introduction

16.2 Methodology for Periodic Flows

16.3 Analytical Predictions

16.4 Numerical Illustrations

16.5 Conclusions

References

17 Impulsive Control Induced Effects on Dynamicsof Complex Networks

17.1 Introduction

17.2 Main Results

17.2.1 Stability Analysis of the Presented Dynamical Networks with Different Dynamical Nodes with Impulsive Control

17.2.2 Impulsive Control Induced Effects on Dynamics of Complex Networks with Identical Dynamical Nodes

17.3 Numerical Simulations

17.4 Conclusion

References

18 Study on Synchronization of Two Identical Uncoupled Neurons Induced by Noise

18.1 Introduction

18.2 Numerical Results and Discussion

18.3 Conclusions

References

19 Non-equilibrium Phase Transitions in a Single-Mode Laser Model Driven by Non-Gaussian Noise

19.1 Introduction

19.2 Approximate Stationary Probability Distribution

19.3 General Analysis

19.4 Conclusion Remarks

References

20 Dynamical Properties of Intensity Fluctuation of Saturation Laser Model Driven by Cross-Correlated Additive and Multiplicative Noises

20.1 Introduction

20.2 Stationary Probability Distribution and Relaxation Time and Correlated Function

20.3 Discussion and Conclusion

References

21 Empirical Mode Decomposition Based on Bistable Stochastic Resonance Denoising

21.1 Introduction

21.2 Empirical Mode Decomposition

21.2.1 IMFs

21.2.2 The Sifting Processing

21.2.3 Examples

21.3 Stochastive Resonance

21.3.1 Bistable System

21.3.2 Examples

21.4 Test of EMD Based on SR Denoising

21.5 Conclusion

References

Part IV Classic Vibrations and Control

22 Order Reduction of a Two-Span Rotor-Bearing System Via the Predictor-Corrector Galerkin Method

22.1 Introduction

22.2 Modeling of the Two-Span Rotor-Bearing System

22.3 The Predictor-Corrector Galerkin Method

22.4 Numerical Results and Discussion

22.5 Conclusions

References

23 Stiffness Nonlinearity Classification Using Morlet Wavelets

23.1 Introduction

23.2 Response of the Nonlinear System

23.3 Wavelet Transform

23.3.1 Wavelet Transform of the Response Signal

23.3.1.1 Standard Morlet Wavelet

23.3.1.2 Complete Morlet Wavelet

23.4 Illustration

23.5 Conclusions

References

24 Dynamics of Wire-Driven Machine Mechanisms: Literature Review

24.1 Introduction

24.2 Mechanical Properties of Wire Ropes

24.2.1 Young's Modulus

24.2.2 Damping

24.3 Dynamics Simulation of Wire Rope Systems

24.3.1 Belt–Pulley Systems

24.3.2 Complex Wire Rope Systems

24.4 Conclusions

References

25 Dynamics of Wire-Driven Machine Mechanisms, Part II: Theory and Applications

25.1 Introduction

25.2 Wire Mechanics

25.2.1 Wire Topology

25.2.2 Elastic Properties of Wire and Chain Elements

25.2.3 Kinematics of Wire Motion

25.2.4 Tension Dynamics

25.3 Boom Mechanics

25.4 Fluid Power Circuit

25.5 System Dynamics Examples

25.5.1 Hydraulic Winch System

25.5.2 Chain Driven Elevating Boom

25.6 Conclusion

References

26 On Analytical Methods for Vibrations of Soils and Foundations

26.1 Introduction

26.2 Surface Response Due to Concentrated Forces

26.3 Dynamic Response of Foundations

26.3.1 Assumed Contact Stress Distributions

26.3.2 Mixed Boundary Value Problems

26.3.3 Lumped Parameter Models

26.3.4 Computational Methods

26.4 Coupled Vibrations of Foundations

26.5 Interactions Between Foundations

26.6 Experimental Studies

26.7 Conclusions

References

27 Inversely Found Elastic and Dimensional Properties

27.1 Introduction

27.2 Computational Overview

27.3 Simplifying Features

27.4 Graphical Relations Between the Cut-Off Frequencies and Cylinder Properties

27.5 Inversion Scheme

27.6 Illustrative Examples

27.6.1 Numerical Simulation

27.6.2 Experimental Corroboration

27.7 Conclusions

References

28 Nonlinear Self-Defined Truss Element Based on the Plane Truss Structure with Flexible Connector

28.1 Introduction

28.2 Finite-Element Dynamic Modeling

28.2.1 Introduction of the Structure

28.2.2 Motion Equations of the Self-Defined Truss Element

28.3 Nonlinear Nodal Forces

28.4 The Numerical Solution Method and Example

28.4.1 The Numerical Solution Method

28.4.2 Numerical Example

28.4.2.1 Random Excitation

28.4.2.2 Contact Stiffness

28.4.2.3 Clearance

28.5 Conclusions

References

29 Complex Frequency Analysis of an Axially Moving String with Multiple Attached Oscillators by Using Green's Function Method

29.1 Introduction

29.2 Formulation of the Eigenvalue Problem

29.3 Construction of Green's Function

29.4 Results and Discussions

29.5 Conclusion

References

30 Model Reduction on Inertial Manifolds of Navier–Stokes Equations Through Multi-scale Finite Element

30.1 Introduction

30.2 Multilevel Finite Element Method

30.3 The Weak Form of the Navier–Stokes Equations

30.4 Numerical Methods

30.5 Large Eddy and Small Eddy Components

30.6 Numerical Examples

30.7 Concluding Remarks

References

31 Diesel Engine Condition Classification Based on Mechanical Dynamics and Time-Frequency Image Processing

31.1 Introduction

31.2 Diesel Engine Structure Dynamics

31.3 Classification by Time Frequency Image

31.3.1 Hilbert Time-Frequency Spectrum

31.3.2 Euclidean Distance

31.3.3 Condition Classification

31.4 Example Analysis

31.4.1 Experiment

31.4.2 Vibration Signal Analysis

31.4.3 Hilbert Spectrum Recognition

31.4.4 ED Discriminant

31.5 Conclusions

References

32 Input Design for Systems Under Identification as Applied to Ultrasonic Transducers

32.1 Introduction

32.2 Input Design Formulation for ARX Models

32.3 System Identification Algorithm

32.4 Input Design for System Identification

32.5 Experimental Results

32.6 Conclusions and Recommendations

References

33 Development of a Control System for Automating of SpiralConcentrators in Coal Preparation Plants

33.1 Introduction

33.2 Technical Approach

33.2.1 Metal Arms and Wheatstone Bridge

33.2.2 Differential Amplifiers

33.2.3 PIC Microcontroller and Motor

33.2.4 Demonstration

33.2.5 Assembly

33.3 Mechanical System Design

33.4 The Need for a Model

33.5 Conclusions

References

34 On the Rough Number Computation and the Ada Language

34.1 Introduction

34.2 Some Basic Algebraic Structures

34.3 The Structure of Dyadic Numbers

34.4 The Structure of Rough Numbers

34.5 Hierarchical Classes and Computation

34.6 The Ada Language and Rough Number Computation

34.7 Conclusions

References

Author Index

Subject Index