HIGH SPEED RAILWAY TRACK DYNAMICS models, algorithms and applications.

Foreword
Preface
About This Book
Description of the Revised Edition
Contents
About the Author
1 Track Dynamics Research Contents and Related Standards
	1.1 A Review of Track Dynamics Research
	1.2 Track Dynamics Research Contents
	1.3 Limits for Safety and Riding Quality
		1.3.1 Safety Limit for Regular Trains
		1.3.2 Riding Quality Limits for Regular Trains
		1.3.3 Safety and Riding Quality Limit for Rising Speed Trains
	1.4 Standards of Track Maintenance for High-Speed Railway
		1.4.1 Standards of Track Maintenance and Management for French High-Speed Railway
		1.4.2 Standards of Track Maintenance and Management for Japanese Shinkansen High-Speed Railway
		1.4.3 Standards of Track Maintenance and Management for German High-Speed Railway
		1.4.4 Standards of Track Maintenance and Management for British High-Speed Railway
		1.4.5 Standards of Measuring Track Geometry for Korean High-Speed Railway (Dynamic)
		1.4.6 Standards of Track Maintenance and Management for Chinese High-Speed Railway
		1.4.7 Dominant Frequency Range and Sensitive Wavelength of European High-Speed Train and Track Coupling System
	1.5 Railway Environmental Noise Standards
		1.5.1 Noise Evaluation Index
		1.5.2 Railway Noise Standards in China
		1.5.3 Railway Noise Standards in Foreign Countries
	1.6 Railway Environmental Vibration Standards
		1.6.1 Vibration Parameter and Evaluation Index
		1.6.2 Environmental Vibration Standards in China’s Urban Areas
		1.6.3 Limit for Building Vibration Caused by Urban Mass Transit
	1.7 Vibration Standards of Historic Building Structures
	References
2 Analytic Method for Dynamic Analysis of the Track Structure
	2.1 Studies of Ground Surface Wave and Strong Track Vibration Induced by High-Speed Train
		2.1.1 Continuous Elastic Beam Model of Track Structure
		2.1.2 Track Equivalent Stiffness and Track Foundation Elasticity Modulus
		2.1.3 Track Critical Velocity
		2.1.4 Analysis of Strong Track Vibration
	2.2 Effects of the Track Stiffness Abrupt Change on Track Vibration
		2.2.1 Track Vibration Model with  Consideration of Track Irregularity and Stiffness Abrupt Change Under Moving Loads
		2.2.2 Reasonable Distribution of the Track Stiffness in Transition
	References
3 Fourier Transform Method for Dynamic Analysis of the Track Structure
	3.1 Model of Single-Layer Continuous Elastic Beam for the Track Structure
		3.1.1 Fourier Transform
		3.1.2 Inverse Discrete Fourier Transform
		3.1.3 Definition of Inverse Discrete Fourier Transform in Matlab
	3.2 Model of Double Layer Continuous Elastic Beam for the Track Structure
	3.3 Analysis of High Speed Railway Track Critical Velocity
		3.3.1 Analysis of the Single-Layer Continuous Elastic beam Model
		3.3.2 Analysis of the Double-Layer Continuous Elastic Beam Model
	3.4 Model of Three-Layer Continuous Elastic Beam for the Track Structure
		3.4.1 Model of Three- Layer Continuous Elastic Beam for the Ballast Track Structure
		3.4.2 Model of Three-Layer Continuous Elastic Beam for the Slab Track Structure
	3.5 Vibration Analysis of the Slab Track Structure
	3.6 Vibration Analysis of Track Structure for Railways with Mixed Passenger and Freight Traffic
	References
4 Analysis of Vibration Behavior of the Elevated Track Structure
	4.1 Basic Concept of Admittance
		4.1.1 Definition of Admittance
		4.1.2 Computational Method of Admittance
		4.1.3 Harmonic Response Analysis
	4.2 Analysis of Vibration Behavior of the Elevated Bridge Structure
		4.2.1 Analytic Beam Model
		4.2.2 Finite Element Model
		4.2.3 Comparison Between the Analytic Model and the Finite Element Model for the Elevated Track-Bridge system
		4.2.4 Influence of the Bridge Bearing Stiffness
		4.2.5 Influence of the Bridge Cross Section Model
	4.3 Analysis of Vibration Behavior of the Elevated Track Structure
		4.3.1 Analytic Model of the Elevated Track-Bridge System
		4.3.2 Finite Element Model
		4.3.3 Damping of the Bridge Structure
		4.3.4 Parameter Analysis of the Elevated Track-Bridge System
	4.4 Analysis of Vibration Attenuation Behavior of the Elevated Track Structure
		4.4.1 Attenuation Rate of Vibration Transmission
		4.4.2 Attenuation Coefficient of Rail Vibration
	References
5 Track Irregularity Power Spectrum and Numerical Simulation
	5.1 Basic Concept of Random Process
		5.1.1 Stationary Random Process
		5.1.2 Ergodic
	5.2 Random Irregularity Power Spectrum of the Track Structure
		5.2.1 American Track Irregularity Power Spectrum
		5.2.2 Germany Track Irregularity Power Spectrum for High-Speed Railway
		5.2.3 Japanese Track Irregularity Sato Power Spectrum
		5.2.4 Chinese Track Irregularity Power Spectrum
		5.2.5 Track Irregularity Power Spectrum for Hefei–Wuhan Passenger Dedicated Line
		5.2.6 Comparison of the Track Irregularity Power Spectrum Fitting Curves
	5.3 Numerical Simulation for Random Irregularity of the Track Structure
	5.4 Trigonometric Series Method
		5.4.1 Trigonometric Series Method (1)
		5.4.2 Trigonometric Series Method (2)
		5.4.3 Trigonometric Series Method (3)
		5.4.4 Trigonometric Series Method (4)
	5.5 Sample of the Track Structure Random Irregularity
	References
6 Vertical Vibration Model for the Track Structure and the Vehicle
	6.1 Fundamental Theory of Dynamic Finite Element Method
		6.1.1 A Brief Introduction to Dynamic Finite Element Method
		6.1.2 Beam Element Theory
	6.2 Finite Element equation of the Track Structure
		6.2.1 Basic Assumptions
		6.2.2 Generalized Beam Element Model of the Track Structure
	6.3 Model of the Track Structure Under Moving Axle Loads
	6.4 Vehicle Model of a Single Wheel with Primary Suspension System
	6.5 Vehicle Model of Half a Car with Primary and Secondary Suspension System
	6.6 Vehicle Model of a Whole Car with Primary and Secondary Suspension System
	6.7 Parameters for the Vehicle and the Track Structure
		6.7.1 Parameters of the Locomotive and Vehicle
		6.7.2 Parameters of the Track Structure
	References
7 A Cross-Iteration Algorithm for Vehicle–Track Nonlinear Coupling Vibration Analysis
	7.1 A Cross-Iteration Algorithm for Vehicle–Track Nonlinear Coupling System
	7.2 Algorithm Validation
		7.2.1 Example Verification
		7.2.2 Influence of the Time Step
		7.2.3 Influence of the Convergence Precision
	7.3 Dynamic Analysis of the Train–Track Nonlinear Coupling System
	7.4 Dynamic Analysis of the Vehicle–Track–Bridge Nonlinear Coupling System
	7.5 Conclusions
	References
8 Moving Element Model and Its Algorithm
	8.1 Moving Wheel Element Model
	8.2 Moving Element Model of a Single Wheel with Primary Suspension System
	8.3 Moving Element Model of a Single Wheel with Primary and Secondary Suspension System
	8.4 Model and Algorithm for Dynamic Analysis of a Single Wheel Moving on the Bridge
	8.5 Vibration Analysis of the Train–Track–Bridge Coupling System
	References
9 Model and Algorithm for Track Element and Vehicle Element
	9.1 Ballast Track Element Model
		9.1.1 Basic Assumptions
		9.1.2 Three-Layer Ballast Track Element
	9.2 Slab Track Element Model
		9.2.1 Basic Assumptions
		9.2.2 Three-Layer Slab Track Element Model
		9.2.3 Mass Matrix of the Slab Track Element
		9.2.4 Stiffness Matrix of the Slab Track Element
		9.2.5 Damping Matrix of the Slab Track Element
	9.3 Slab Track–Bridge Element Model
		9.3.1 Basic Assumptions
		9.3.2 Three-Layer Slab Track and Bridge Element Model
		9.3.3 Mass Matrix of the Slab Track–Bridge Element
		9.3.4 Stiffness Matrix of the Slab Track–Bridge Element
		9.3.5 Damping Matrix of the Slab Track–Bride Element
	9.4 Vehicle Element Model
		9.4.1 Potential Energy of the Vehicle Element
		9.4.2 Kinetic Energy of the Vehicle Element
		9.4.3 Dissipated Energy of the Vehicle Element
	9.5 Finite Element Equation of the Vehicle–Track Coupling System
	9.6 Dynamic Analysis of the Train-Track Coupling System
	References
10 Dynamic Analysis of the Vehicle–Track Coupling System with Finite Elements in a Moving Frame of Reference
	10.1 Basic Assumptions
	10.2 Three-Layer Beam Element Model of the Slab Track in a Moving Frame of Reference
		10.2.1 Governing Equation of the Slab Track
		10.2.2 Element Mass, Damping and Stiffness Matrixes of the Slab Track in a Moving Frame of Reference
	10.3 Vehicle Element Model
	10.4 Finite Element Equation of the Vehicle–Slab Track Coupling System
	10.5 Algorithm Verification
	10.6 Dynamic Analysis of the High-Speed Train-Slab Track Coupling System
	References
11 Model for Vertical Dynamic Analysis of the Vehicle–Track–Subgrade–Ground Coupling System
	11.1 Model of the Slab Track–Embankment–Ground System Under Moving Loads
		11.1.1 Dynamic Equation and Its Solution for the Slab Track–Subgrade Bed System
		11.1.2 Dynamic Equation and Its Solution for the Embankment Body-Ground System
		11.1.3 Coupling Vibration of the Slab Track–Embankment–Ground System
	11.2 Model of the Ballast Track–Embankment–Ground System Under Moving Loads
		11.2.1 Dynamic Equation and Its Solution for the Ballast Track–Subgrade Bed System
		11.2.2 Coupling Vibration of the Ballast Track–Embankment–Ground System
	11.3 Analytic Vibration Model of the Moving Vehicle–Track–Subgrade–Ground Coupling System
		11.3.1 Flexibility Matrix of the Moving Vehicles at Wheelset Points
		11.3.2 Flexibility Matrix of the Track–Subgrade–Ground System at Wheel–Rail Contact Points
		11.3.3 Coupling of the Moving Vehicle–Subgrade–Ground System by Consideration of Track Irregularities
	11.4 Dynamic Analysis of the High-Speed Train–Track–Subgrade–Ground Coupling System
		11.4.1 Influence of the Train Speed and Track Irregularity on Embankment Body Vibration
		11.4.2 Influence of the Subgrade Bed Stiffness on Embankment Body Vibration
		11.4.3 Influence of the Embankment Soil Stiffness on Embankment Body Vibration
	References
12 Analysis of Dynamic Behavior of the Train, Ballast Track and Subgrade Coupling System
	12.1 Parameters for Vehicle and Track Structure
	12.2 Influence Analysis of the Train Speed
	12.3 Influence Analysis of the Track Stiffness Distribution
	12.4 Influence Analysis of the Transition Irregularity
	12.5 Influence Analysis of the Combined Track Stiffness and Transition Irregularity
	References
13 Analysis of Dynamic Behavior of the Train-Slab Track-Subgrade Coupling System
	13.1 Example Validation
	13.2 Parameter Analysis of the Dynamic Behavior of the Train-Slab Track-Subgrade Coupling System
	13.3 Influence of the Rail Pad and Fastener Stiffness
	13.4 Influence of the Rail Pad and Fastener Damping
	13.5 Influence of the CA Mortar Stiffness
	13.6 Influence of the CA Mortar Damping
	13.7 Influence of the Subgrade Stiffness
	13.8 Influence of the Subgrade Damping
	References
14 Analysis of Dynamic Behavior of the Transition Section Between Ballast Track and Ballastless Track
	14.1 Influence Analysis of the Train Speed for the Transition Section Between the Ballast Track and the Ballastless Track
	14.2 Influence Analysis of the Track Foundation Stiffness for the Transition Section Between the Ballast Track and the Ballastless Track
	14.3  Remediation Measures of the Transition Section Between the Ballast Track and the Ballastless Track
	References
15 Analysis of Medium and High-Frequency Vibration for Track Structure
	15.1 Introduction
	15.2 Single-Layer Beam Model for Track Structure
		15.2.1 Spectral Element Stiffness Matrix of the Single-Layer Beam Model for Track Structure
		15.2.2 Spectral Element Stiffness Matrix of the Rail Pad and Fastener
		15.2.3 Spectral Element Stiffness Matrix of 2D Truncation Beam Element
		15.2.4 Spectral Stiffness Matrix of the Global Structure
	15.3 Spectral Element Stiffness Matrix of the Three-Layer Beam Model for Slab Track Structure
	15.4 Vibration Analysis of the Track Structure with the Single-Layer Beam Spectral Element Model
	15.5 Parameter Analyses of Medium and High-Frequency Vibration for the Slab Track Structure
		15.5.1 Effect of the Rail Pad and Fastener Stiffness
		15.5.2 Effect of the CA Asphalt Mortar Stiffness
		15.5.3 Effect of the Subgrade Stiffness
		15.5.4 Brief Summary
	15.6 Frequency Domain Method for Dynamic Analysis of the Vehicle–Track Coupling System
		15.6.1 Vehicle Model
		15.6.2 Spectral Element Equation of the Vehicle–Track Coupling System
	15.7 Frequency Domain Analysis of the Dynamic Response of the Vehicle–Track Coupling System
		15.7.1 Model Verification
		15.7.2 Frequency Domain Analysis of the Dynamic Response of the Vehicle–Track Coupling System
		15.7.3 Analysis of Vertical Vibration of the Wheelset and the Rail
		15.7.4 Analysis of Vibration Attenuation of the Track Structure
		15.7.5 Conclusions
	References
Appendix A Parameters of Vehicle and Track Structure
Appendix B Slab Track Dynamics Calculation Program STDYN1.0
B.1 Model Introduction
B.2 Program Description
Appendix C Train-Track-Continuous Bridge Coupling System Dynamics Calculation Program VTBDYN1.0
C.1 Model Introduction
C2. Program Description
Appendix D Dynamics Calculation Program WTBDYN1.0 for the Moving Wheelset with Primary and Secondary Suspension–Track–Continuous Bridge Coupling System
D.1 Model Introduction
D.2 Program Description
Index