Contents
1 Track Dynamics Research Contents and Related Standards 1
1.1 A Review of Track Dynamics Research 1
1.2 Track Dynamics Research Contents 6
1.3 Limits for Safety and Riding Quality 7
1.3.1 Safety Limit for Regular Trains 7
1.3.2 Riding Quality Limits for Regular Trains 8
1.3.3 Safety and Riding Quality Limit for Rising Speed Trains 10
1.4 Standards of Track Maintenance for High-Speed Railway 11
1.4.1 Standards of Track Maintenance and Management for French High-Speed Railway 12
1.4.2 Standards of Track Maintenance and Management for Japanese Shinkansen High-Speed Railway 13
1.4.3 Standards of Track Maintenance and Management for German High-Speed Railway 13
1.4.4 Standards of Track Maintenance and Management for British High-Speed Railway 13
1.4.5 Standards of Measuring Track Geometry for Korean High-Speed Railway (Dynamic) 16
1.4.6 Standards of Track Maintenance and Management for Chinese High-Speed Railway 16
1.4.7 Dominant Frequency Range and Sensitive Wavelength of European High-Speed Train and Track Coupling System 18
1.5 Railway Environmental Noise Standards 19
1.5.1 Noise Evaluation Index 19
1.5.2 Railway Noise Standards in China 20
1.5.3 Railway Noise Standards in Foreign Countries 20
1.6 Railway Environmental Vibration Standards 21
1.6.1 Vibration Parameter and Evaluation Index 21
1.6.2 Environmental Vibration Standards in China’s Urban Areas 29
1.6.3 Limit for Building Vibration Caused by Urban Mass Transit 29
1.7 Vibration Standards of Historic Building Structures 31
References 36
2 Analytic Method for Dynamic Analysis of the Track Structure 41
2.1 Studies of Ground Surface Wave and Strong Track Vibration Induced by High-Speed Train 41
2.1.1 Continuous Elastic Beam Model of Track Structure 42
2.1.2 Track Equivalent Stiffness and Track Foundation Elasticity Modulus 44
2.1.3 Track Critical Velocity 45
2.1.4 Analysis of Strong Track Vibration 45
2.2 Effects of the Track Stiffness Abrupt Change on Track Vibration 48
2.2.1 Track Vibration Model with Consideration of Track Irregularity and Stiffness Abrupt Change Under Moving Loads 48
2.2.2 Reasonable Distribution of the Track Stiffness in Transition 55 References 59
3 Fourier Transform Method for Dynamic Analysis of the Track Structure 61
3.1 Model of Single-Layer Continuous Elastic Beam for the Track Structure 61
3.1.1 Fourier Transform 62
3.1.2 Inverse Discrete Fourier Transform 64
3.1.3 De.nition of Inverse Discrete Fourier Transform in Matlab 65
3.2 Model of Double Layer Continuous Elastic Beam for the Track Structure 66
3.3 Analysis of High Speed Railway Track Critical Velocity 68
3.3.1 Analysis of the Single-Layer Continuous Elastic beam Model 69
3.3.2 Analysis of the Double-Layer Continuous Elastic Beam Model 71
3.4 Model of Three-Layer Continuous Elastic Beam for the Track Structure 72
3.4.1 Model of Three-Layer Continuous Elastic Beam for the Ballast Track Structure 75
3.4.2 Model of Three-Layer Continuous Elastic Beam for the Slab Track Structure 79
3.5 Vibration Analysis of the Slab Track Structure 81
3.6 Vibration Analysis of Track Structure for Railways with Mixed Passenger and Freight Traffic 82
References 89
4 Analysis of Vibration Behavior of the Elevated Track Structure 91
4.1 Basic Concept of Admittance 91
4.1.1 Definition of Admittance 91
4.1.2 Computational Method of Admittance 92
4.1.3 Harmonic Response Analysis 93
4.2 Analysis of Vibration Behavior of the Elevated Bridge Structure 94
4.2.1 Analytic Beam Model 95
4.2.2 Finite Element Model 99
4.2.3 Comparison Between the Analytic Model and the Finite Element Model for the Elevated Track-Bridge system 99
4.2.4 Influence of the Bridge Bearing Stiffiiess 101
4.2.5 Influence of the Bridge Cross Section Model 102
4.3 Analysis of Vibration Behavior of the Elevated Track Structure 103
4.3.1 Analytic Model of the Elevated Track-Bridge System 103
4.3.2 Finite Element Model 108
4.3.3 Damping of the Bridge Structure 109
4.3.4 Parameter Analysis of the Elevated Track-Bridge System 111
4.4 Analysis of Vibration Attenuation Behavior of the Elevated Track Structure 115
4.4.1 Attenuation Rate of\\^bration Transmission 115
4.4.2 Attenuation Coefficient of Rail Vibration 119
References 120
5 Track Irregularity Power Spectrum and Numerical Simulation 121
5.1 Basic Concept of Random Process 122
5.1.1 Stationary Random Process 123
5.1.2 Ergodic 124
5.2 Random Irregularity Power Spectrum of the Track Structure 124
5.2.1 American Track Irregularity Power Spectrum 125
5.2.2 Germany Track Irregularity Power Spectrum
for High-Speed Railway 126
5.2.3 Japanese Track Irregularity Sato Power Spectrum 127
5.2.4 Chinese Track Irregularity Power Spectrum 127
5.2.5 Track Irregularity Power Spectrum for Hefei-Wuhan Passenger Dedicated Line 131
5.2.6 Comparison of the T
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