NONLINEAR APPROACHES IN ENGINEERING APPLICATIONS : design engineering problems

Nonlinear Approaches in Engineering Applications: Design Engineering Problems examines the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Chapters are authored by world-class scientists and researchers and focus on the application of nonlinear approaches in different disciplines of engineering and scientific applications, with a strong emphasis on application, physical meaning, and methodologies of the approaches. Topics covered are of high interest in engineering and physics, and an attempt has been made to expose engineers and researchers to a broad range of practical topics and approaches. This book is appropriate for researchers, students, and practicing engineers who are interested in the applications of engineering, physics, and mathematics in nonlinear approaches to solving engineering and science problems. Preface Level of the Book Organization of the Book Method of Presentation Prerequisites Acknowledgments Contents List of Figures Part I Modeling of Engineering Design Problems 1 Improved Theoretical and Numerical Approaches for Solving Linear and Nonlinear Dynamic Systems 1.1 Introduction 1.2 Fundamental Theory 1.2.1 Piecewise Constant Argument 1.2.2 Laplace Transformation and Residues Principle 1.2.3 The Periodicity Ratio of Nonautonomous Systems 1.2.4 The Periodicity Ratio of Autonomous Systems 1.3 Analytical and Numerical Solutions of Stiffness Coupling Systems 1.3.1 Stiffness Coupling System 1.3.2 Stiffness and Damping Coupling System 1.3.3 Stiffness and Damping Coupling System with External Excitation 1.3.4 Convergence Analysis of the PL Method 1.4 Analytical and Numerical Solutions of Inertial Coupling Systems 1.4.1 Undamped Inertial Coupling System 1.4.2 Damped Inertial Coupling System 1.4.3 Forced and Damped Inertial Coupling System 1.4.4 Convergence Analysis of the PL Method 1.5 Diagnosing Irregularities of Nonlinear Systems 1.5.1 Nonlinear Nonautonomous System 1.5.2 Nonlinear Autonomous System 1.6 Conclusion References 2 Novel Predictor-Corrector Formulations for Solving Nonlinear Initial Value Problems 2.1 Introduction 2.2 Bezier Curves 2.3 Multistep Method 2.4 Methodology 2.5 Stability Analysis 2.6 Numerical Experiments 2.6.1 Duffing Equation 2.6.2 Van Der Pol Equation 2.7 Conclusion References 3 Control of Nonhyperbolic Dynamical Systems Through Center Manifold Control 3.1 Introduction 3.2 Control of Dynamical Systems with Nonhyperbolic Equilibrium Points 3.3 Conclusions References 4 Linear and Nonlinear Aspects of Space Charge Phenomena Abbreviations Nomenclature 4.1 Introduction 4.2 Spacecraft Charging Effects on Dielectric Materials 4.3 Space Charge Behavior of Dielectric Nanocomposites 4.4 Mitigation Methods 4.4.1 Active Mitigation Methods 4.4.2 Passive Mitigation Methods 4.5 Impact of Space Radiation on Ionic Materials 4.6 Nonlinear Phenomena in Space Charge 4.7 Conclusions References 5 Inertial Morphing as a Novel Concept in Attitude Control and Design of Variable Agility Acrobatic Autonomous Spacecraft 5.1 Introduction 5.2 Historical Background 5.2.1 Discovery of the “Garriott's-Dzhanibekov's Effect” in Space 5.2.2 Demonstrations of the “Garriott's-Dzhanibekov's Effect” on-Board of the ISS 5.2.3 Leonard Euler and His Famous Equations for the Rigid-Body Dynamics 5.3 Numerical Modelling and Simulation of the “Garriott's-Dzhanibekov's Effect” 5.3.1 Equations of Motion 5.3.2 Programming Considerations 5.3.3 Non-dimensional Formulation of the Equations 5.3.4 Numerical Simulation of the “Garriott's-Dzhanibekov's Effect”: Illustration Case 5.4 Calculation of the Period of the Flipping Motion 5.4.1 Influence of the Value of the Angular Velocity y of the Predominant Spin on the Period T of the Flipping Motion 5.4.2 Influence of the Value of the Period T of the Flipping Motion on the Angular Velocity y of the Predominant Spin 5.5 Geometric Interpretation of the 3D Rotational Dynamics of Rigid Objects 5.5.1 General Comments 5.5.2 Angular Momentum Sphere 5.5.3 Utilisation Angular Momentum Sphere and Its Feasible Godographs for the Non-dimensional Angular Momentum Vector as Strategic Basis for the Methods of Attitude Control of the Rotating Systems 5.5.4 Polhodes on the Angular Momentum Sphere 5.5.5 Kinetic Energy Ellipsoid 5.5.6 Polhodes on the Kinetic Energy Ellipsoids 5.5.7 Polhodes for Systems with Equal Moments of Inertia 5.6 Geometric Interpretation of the “Garriott's-Dzhanibekov's Effect”, Using Angular Momentum Sphere and Kinetic Energy Ellipsoid 5.6.1 Collocated Angular Momentum Sphere and Kinetic Energy Ellipsoid for the Garriott's-Dzhanibekov's Flipping Motion Example 5.6.2 Conceptual Spacecraft Model, Based on the Flipping Motion 5.6.3 Investigating Orientation of the Sides of the Spacecraft Exposed to the Specific Directions 5.7 Proposing New Spacecraft Designs/Missions, Utilising Garriott's-Dzhanibekov's Effect and Inertial Morphing 5.7.1 Proposing Method of “Switching ON/OFF” Garriott's-Dzhanibekov's Spacecraft Flipping Motion by Controlled Inertial Morphing 5.7.2 Extending Euler's Equations for Rigid-Body Rotations, Allowing Variation of Moments of Inertia 5.7.3 Six-Mass Conceptual Model of the Spacecraft with Inertial Morphing Capabilities 5.7.4 Conceptual Example of the Morphed Spacecraft, Self-Transferring from Unstable Flipping Motion to Stable No-Flips Spin 5.7.5 Geometric Interpretation of the Cases, Where “Garriott's-Dzhanibekov's Effect” Is Controlled 5.7.5.1 Stopping Flipping Motion, Using One Inertial Morphing: Solution-1 5.7.5.2 Stopping Flipping Motion, Using One Inertial Morphing: Solution-2 5.8 Attitude Dynamics of Spacecraft with Inertial Morphing 5.8.1 Study Case-2: “Switching OFF” Flipping Motion of the Spacecraft After One Flip (Solution-1) 5.8.2 Study Case-3: “Switching OFF” Flipping Motion of the Spacecraft After One Flip (Solution-2) 5.8.3 Study Case-4: “Switching OFF” Flipping Motion of the Spacecraft After Two Flips (Solution-1) 5.8.4 Study Case-5: “Switching ON” Spacecraft Flipping Motion 5.8.5 Study Case-6: “Switching ON” Spacecraft Flipping Motion with Following One Flip and “Switching OFF” 5.8.6 Study Case-7: Control of the Frequency of the Flipping Motion via “Inertial Morphing” 5.9 Inertial Morphing and the Law of Conservation of Angular Momentum 5.10 Inertial Morphing in Novel Designs of Acrobatic Spacecraft for 180 Degrees Inversions: Method of “Installing into Separatrix” with Pole-Separatrix-Pole Transfer 5.10.1 Applications of Acrobatic Missions 5.10.2 Illustrated Description of Application of IM for Thruster Direction Control 5.10.3 Fast 180 Degrees Inversion of the Spacecraft 5.10.4 Slow 180 Degrees Inversion of the Spacecraft (Figs. 5.44, 5.45 and 5.46) 5.11 Inertial Morphing in Novel Designs of Acrobatic Spacecraft for De-tumbling: Method of “Installing into Separatrix” with Polhode-Separatrix-Pole or Polhode-Polhode-Separatrix-Pole Transfer 5.11.1 Application of Inertial Morphing to the Tumbling Spacecraft Model: Observations 5.11.2 Formulation of the Conceptual Solution for De-tumbling of the Spacecraft, Using “Installing into Polhode” via “Polhode-to-Polhode” Transfer 5.11.3 Detailed Example on “Installing into Polhode” via “Polhode-to-Polhode” Transfer (Fig. 5.55) 5.11.4 Control Method of Installing into Separatrix Using Inertial Morphing: Geometric Interpretation 5.11.5 Control Method of Installing into Separatrix, Using Inertial Morphing: Selection of the IM Parameters and IM Activation Time 5.11.6 Example of the “Flipping”-Assisted Stabilisation (De-tumbling) of the Tumbling Spacecraft, Using Inertial Morphing 5.11.7 Reversing Vector of Angular Momentum on the Separatrix, Installing Its Godograph into the Same Separatrix 5.11.8 Summary of the Method of Installing of the Godograph of the Non-dimensional Vector of Angular Momentum of Tumbling Spacecraft into Conjugate Separatrix 5.12 Inertial Morphing in Novel Designs of Acrobatic Spacecraft for 90 Degrees Inversions: Method of “Installing into Separatrix” with Separatrix-to-Separatrix Transfer 5.13 Demo of Combined Multiphase Inertial Morphing: Consecutive “Parade” of All Three Orthogonal Inversions, Associated with x, y and z Body Axes 5.14 Enhancement of the Reorientation and Change of the Spin Axis Using Moment Wheel 5.15 Animations in Virtual Reality 5.16 Examples of the Conceptual Designs of the Inertially Morphed Systems 5.16.1 Example-1 Design, Involving “Six-Masses” Repositioned Along Body Axes 5.16.2 Example-2 Design: “Scissors” Model for Inertial Morphing 5.16.3 Example-3 Design: Rhombus Model for Inertial Morphing 5.16.4 Example-4 Design: Two Cylinders System 5.16.5 Suggestions on Some Practical Implementation of the Inertial Morphing 5.17 Conclusions Appendixes Nomenclature Acronyms/Abbreviations References 6 A New Strategy for Form Finding and Optimal Design of Space Cable Network Structures 6.1 Introduction 6.2 Problem Statement 6.2.1 Four Types of Structural Assemblies and Extended Maxwell's Rule 6.2.2 Cable Network, Tensegrity, and Truss Structures 6.2.3 Geometric and Force Constraints 6.2.4 Desired Internal Force Distribution 6.3 The Fixed Nodal Position Method for FF-IEC 6.3.1 Initial Guess of Geometric Configuration 6.3.2 Determination of Internal Force Distribution 6.3.3 Adaptation of Geometric Configuration 6.3.4 Procedure of the FNPM 6.4 Review of the Force Density Method and Dynamic Relaxation Method for FF-IEC 6.4.1 The Force Density Method 6.4.2 The Dynamic Relaxation Method 6.5 Methods of FF-DEC 6.5.1 Singular Value Decomposition Method 6.5.2 Stiffness Matrix Method 6.5.3 Dynamic Relaxation Method 6.6 Implementation of the Form-Finding Methods 6.6.1 FF-IEC of a 2-D Cable Net 6.6.1.1 The Fixed Nodal Position Method 6.6.1.2 The Force Density Method 6.6.1.3 The Dynamic Relaxation Method 6.6.2 FF-DEC of a 2-D cable net 6.6.2.1 The Singular Value Decomposition Method 6.6.2.2 The Stiffness Matrix Method 6.6.2.3 The Dynamic Relaxation Method 6.6.3 Form Finding of a Large Deployable Mesh Reflector of 865 Nodes 6.7 Conclusions Appendix Global Minimizer and Solution of the Optimization Problem (6Equ126.12) References Part II Applied Design of Engineering Problems 7 Application of Genetic Algorithm in Characterisation of Geometry Welds in Spot Weld Process Design 7.1 Introduction 7.1.1 Statement of the Problem 7.1.2 Research Objectives 7.1.3 Research Questions 7.2 Background 7.2.1 Assembly Sequence Planning (ASP) 7.2.1.1 Assembly Plans 7.2.1.2 The Assembly Sequence Planning Problem 7.2.1.3 Solving the Assembly Sequence Planning Problem 7.2.1.4 ASP Optimisation 7.2.2 Automotive Body Welding Optimisation 7.3 Optimisation of the Body Processes Using Genetic Algorithm 7.3.1 Genetic Algorithm and Its Applications 7.3.2 GA Constraint Handling Methods 7.3.3 Body Process Modelling for Genetic Algorithm Analysis 7.3.3.1 Genetic Algorithm Platforms 7.3.3.2 GA Model Development References 8 The Past, Present and Future of Motion Sickness in Land Vehicles 8.1 Introduction 8.2 What Was Motion Sickness in Land Vehicles of Old? 8.3 What Is Motion Sickness in Cars of Today? 8.4 What Motion Sickness Beholds in Cars of Future? References 9 Vehicle Vibration Analysis of the Quarter-Car Model Considering Tire-Road Separation 9.1 Introduction 9.2 Dynamic Equations of Motion 9.3 Time Response 9.4 Frequency Domain 9.5 Separation Boundary 9.6 Separation Duration 9.7 Conclusion References 10 Nonlinear Model Predictive Control Real-Time Optimizers for Adaptive Cruise Control: A Comparative Study 10.1 Introduction 10.2 NMPC Formulation and Implementation 10.2.1 Problem Formulation 10.2.2 Applied Algorithms 10.2.3 Implementation of Automatic NMPC Code Generation 10.3 Adaptive Cruise Control Formulation 10.4 Results and Discussion 10.4.1 MIL Simulations 10.4.2 HIL Experiments 10.5 Conclusion and Future Work References 11 Influence of Lateral Asymmetry on Car's Lateral Dynamics 11.1 Introduction 11.2 Modelling 11.3 Lateral Dynamics of Asymmetrical Car 11.3.1 Car's CoG Deviating Toward the Inner 11.3.2 Car's CoG Deviating Toward the Outer 11.4 Conclusion 11.5 Notations References 12 Roll Model Control of Autonomous Vehicle 12.1 Introduction 12.2 Roll Model Equation of Motion 12.3 Steady-State Motion for Roll Model 12.4 Control of Autonomous Vehicles, Autodriver Algorithm and Vehicle Dynamics 12.4.1 Road Geometry 12.4.1.1 Horizontal Curve 12.4.1.2 Road Curvature Modelling 12.4.1.3 Road Curvature Centre 12.4.2 Kinematic Analysis and the Dynamic Vehicle Rotation Centre 12.4.3 Vehicle Dynamics (High-Velocity Manoeuvres) 12.4.4 Autonomous Control 12.4.5 Case Study Scenarios 12.4.5.1 Constant Velocity 12.4.5.2 Nonlinear Varying Steering 12.4.5.3 Nonlinear Variable Velocity 12.4.6 Planar-Roll Vehicle Dynamics 12.4.6.1 Equations of Motion 12.4.6.2 Steady-State Responses 12.4.7 Vehicle Behaviour 12.4.8 Autonomous Control 12.4.8.1 Improved Autodriver Algorithm 12.4.8.2 Calculation of Steady-State Inputs 12.4.8.3 Elimination of Transient Error 12.5 Control 12.5.1 Simulation Results 12.5.2 Figure-8 Road 12.5.3 Lane Change Manoeuvre 12.6 Conclusion References 13 Oil Leakage Analysis for an Active Anti-Roll Bar System of Heavy Vehicles 13.1 Introduction 13.1.1 Rollover of Heavy Vehicles 13.1.2 Different Categories of Vehicle Rollover Accidents 13.1.3 Active Anti-Roll Bar System 13.1.4 Oil Leakage of the Electronic Servo-Valve 13.2 An Electronic Servo-Valve Hydraulic Actuator Model 13.2.1 The Electronic Servo-Valve Model 13.2.2 The Hydraulic Cylinder Model 13.2.3 Internal Leakage Inside the Electronic Servo-Valve 13.3 Vehicle Modelling 13.3.1 The Yaw-Roll Model of a Single Unit Heavy Vehicle 13.3.2 The Fully Integrated Model of a Single Unit Heavy Vehicle 13.4 Effect of the Internal Leakage Inside the Electronic Servo-Valve on the Open-Loop System 13.4.1 Neutral Position of the Spool Valve 13.4.2 Effect of the Internal Leakage on the Open-Loop System 13.4.2.1 Effect of the Internal Leakage Inside the Servo-Valve in the Frequency Domain 13.4.2.2 Effect of the Internal Leakage Inside the Servo-Valve in the Time Domain 13.5 Effect of the Internal Leakage Inside the Electronic Servo-Valve on the Closed-Loop System 13.5.1 H∞/LPV Control Design for the Fully Integrated Model 13.5.2 Simulation Results Analysis with the Nominal Value of the Total Flow Pressure Coefficient 13.5.2.1 Analysis in the Frequency Domain 13.5.2.2 Analysis in the Time Domain 13.5.3 Effect of the Internal Leakage on the Performance of the H∞/LPV Active Anti-Roll Bar Control System 13.5.3.1 Analysis in the Frequency Domain 13.5.3.2 Analysis in the Time Domain 13.6 Conclusion References 14 Thermal Comfort and Game Theory 14.1 Introduction 14.2 Thermal Comfort 14.3 Game Theory 14.4 Proposed Method 14.5 Results and Discussion 14.6 Conclusion and Future Work References 15 Wind Resource Assessment 15.1 Introduction to Wind Speed and Energy 15.2 Wind Patterns Around the Globe 15.2.1 Global Effects 15.2.2 Local Effects 15.2.3 Topographic Speedup 15.3 Estimating Wind Speed with Height, Atmospheric Condition, and Terrain 15.3.1 Air Density Model 15.3.2 Atmospheric Boundary Layer 15.3.3 Wind Profile Models 15.3.4 Characteristics of Terrain 15.4 Wind Variability 15.4.1 Inter-Annual Wind Variability 15.4.2 Annual and Diurnal Wind Variability 15.4.3 Short-Term Wind Variability and Turbulence 15.5 Wind Data Analysis 15.5.1 Statistical Analysis with Direct Use of Data 15.5.2 Statistical Analysis Using Bin Methods 15.5.3 Statistical Analysis Using Wind Speed Probability Density Function 15.6 Conclusions References Index