The first book to comprehensively cover the theories, models, algorithms and engineering applications of high-speed railway track dynamics
This book systematically summarizes the latest research findings on high-speed railway track dynamics, made by the author and his research team over the past decade. It explores cutting-edge issues concerning the basic theory of high-speed railways, covering the dynamic theories, models, algorithms and engineering applications of the high-speed train and track coupling system.
Presenting original concepts, systematic theories and advanced algorithms, the book places great emphasis on the precision and completeness of its content. The chapters are interrelated yet largely self-contained, allowing readers to either read through the book as a whole or focus on specific topics. It also combines theories with practice to effectively introduce readers to the latest research findings and developments in high-speed railway track dynamics. It offers a valuable resource for researchers, postgraduates and engineers in the fields of civil engineering, transportation, highway & railway engineering.
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 and Railway Environmental Standards
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
1.3.4 Railway Noise Standards in China
1.3.5 Railway Noise Standards in Foreign Countries
1.3.6 Noise Limit for Railway Locomotives and Passenger Trains in China
1.3.7 Environmental Vibration Standards in China’s Urban Areas
1.3.8 Limit for Building Vibration Caused by Urban Mass Transit
1.4 Standards of Track Maintenance for High-Speed Railway
1.4.1 Standards of Track Maintenance 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 The Measuring Standards of Track Geometry for Korean High-Speed Railway (Dynamic)
1.4.6 Standards of Track Maintenance for Chinese High-Speed Railway
1.4.7 The Dominant Frequency Range and Sensitive Wavelength of European High-Speed Train and Track Coupling System
1.5 Vibration Standards of Historic Building Structures
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 The 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 Track Stiffness Abrupt Change on Track Vibration.
2.2.1 Track Vibration Model in Considerationof Track Irregularity and Stiffness Abrupt Change Under Moving Loads
2.2.2 The Reasonable Distribution of the Track Stiffness in Transition
3 Fourier Transform Method for Dynamic Analysisof 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 Vibration and Track Critical Velocity
3.3.1 Analysis of the Single-Layer Continuous Elastic Beam Model
3.4 Vibration Analysis of Track for Railways with Mixed Passenger and Freight Traffic
3.4.1 Three-Layer Continuous Elastic Beam Model of Track Structure
3.4.2 Numerical Simulation of Track Random Irregularity
3.4.3 Fourier Transform for Solving Three-Layer Continuous Elastic Beam Model of Track Structure
3.5 Vibration Analysis of Ballast Track with Asphalt Trackbed Over Soft Subgrade.
3.5.1 Four-Layer Continuous Elastic Beam Model of Track Structure
3.5.2 Fourier Transform for Solving Four-Layer Continuous Elastic Beam Model of Track Structure
3.5.3 Vibration Analysis of Ballast Track with Asphalt Trackbed Over Soft Subgrade.
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 Basic Theory of 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 Analytic Model and Finite Element Model of the Elevated Track-Bridge
4.2.4 The Influence of the Bridge Bearing Stiffness
4.2.5 The 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 The Attenuation Rate of Vibration Transmission.
4.4.2 Attenuation Coefficient of Rail Vibration
5 Track Irregularity Power Spectrum and Numerical Simulation
5.1 Basic Concept of Random Process
5.1.1 Stationary Random Process
5.2 Random Irregularity Power Spectrum of the Track Structure
5.2.1 American Track Irregularity Power Spectrum
5.2.2 Track Irregularity Power Spectrum for German High-Speed Railways .
5.2.3 Japanese Track Irregularity Sato Spectrum
5.2.4 Chinese Trunk Track Irregularity Spectrum
5.2.5 The Track Irregularity Spectrum of 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)
5.4.5 Sample of the Track Structure Random
6 Model for Vertical Dynamic Analysis of the Vehicle-Track Coupling System
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 and Computing Model
6.2.2 Theory of Generalized Beam Element of Track Structure
6.3 Model of Track Dynamics 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 Vehicle and Track Structure
6.7.1 Basic Parameters of Locomotives and Vehicles. . .
6.7.2 Basic Parameters of the Track Structure .
7 A Cross-Iteration Algorithm for Vehicle-Track Coupling Vibration Analysis.
7.1 A Cross-Iteration Algorithm for Vehicle-Track Nonlinear Coupling System .
7.2 Example Validation
7.2.2 The Influence of Time Step.
7.2.3 The Influence of Convergence Precision
7.3 Dynamic Analysis of the Train-Track Nonlinear Coupling System
8 Moving Element Model and Its Algorithm
8.1 Moving 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 Systems
8.4 Model and Algorithm for Dynamic Analysis of a Single Wheel Moving on the Bridge
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 and Track Coupling System
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 High-Speed Train and Slab Track Coupling System
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 Moving Vehicles at Wheelset Points
11.3.2 Flexibility Matrix of the Track-Subgrade-Ground System at Wheel-Rail Contact Points
11.4 Dynamic Analysis of the High-Speed Train-Track-Subgrade- Ground Coupling System
11.4.1 Influence of Train Speed and Track Irregularity on Embankment Body Vibration
11.4.2 Influence of Subgrade Bed Stiffness on Embankment Body Vibration
11.4.3 Influence of Embankment Soil Stiffness on Embankment Body Vibration
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
13 Analysis of Dynamic Behavior of the Train, Slab Track, and Subgrade Coupling System
13.1 Example Validation
13.2 Parameter Analysis of Dynamic Behavior of the Train, Slab Track, and 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 .
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 .
15 Environmental Vibration Analysis Induced by Overlapping Subways
15.1 Vibration Analysis of the Ground Induced by Overlapping Subways
15.1.1 Project Profile
15.1.2 Material Parameters .
15.1.3 Finite Element Model
15.1.4 Damping Coefficient and Integration Step
15.1.5 Vehicle Dynamic Load
15.1.6 Environmental Vibration Evaluation Index .
15.1.7 Influence of Operation Direction of Uplink and Downlink on Vibration
15.1.8 Vibration Reduction Scheme Analysis for Overlapping Subways
15.1.9 Vibration Frequency Analysis
15.1.10 Ground Vibration Distribution Characteristics
15.2 Vibration Analysis of the Historic Building Induced by Overlapping Subways
15.2.1 Project Profile
15.2.2 Finite Element Model
15.2.3 Modal Analysis of Building
15.2.4 Horizontal Vibration Analysis of the Building.
15.2.5 Vertical Vibration Analysis of the Building.