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研究生：	林宏達 Lin, Hung-Ta
論文名稱：	橋樑與地表面於移動列車作用下空間振動反應之研究 Study on Spatial Vibration Responses of Bridges and Ground Surface Under Moving Trains
指導教授：	朱聖浩 Ju, Sheng-Haw
學位類別：	博士 Doctor
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	209
中文關鍵詞：	大底版、雷利波速、共振、地表面、高速列車、橋樑
外文關鍵詞：	foundation slab, Rayleigh wave speed, resonance, bridge, high-speed train, ground surface
相關次數：	點閱：97 下載：5
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移動中的高速列車會使橋樑產生明顯的振動。因此，如何去減少高速列車所導致之振動，將成為一個非常重要的課題。首先，這篇論文推導了一個簡單的移動車輪有限元素分析模型，並以一組移動車輛去模擬移動中的高速列車問題。然後，使用三維有限元素法去分析列車車速與橋樑兩者間產生共振的相互關係，所分析的橋樑型式包括有多跨的簡支樑橋、拱橋和斜張橋。由分析結果顯示，對於橋樑振動而言，共振是一個重要的問題。所以，為了使多跨的簡支樑橋避免發生列車-橋樑的共振，應使得列車的頻率與橋樑在每個方向上的第一個自然頻率儘可能不要相同。假如兩者的第一個頻率相近時，則橋樑的共振現象將為更嚴重。對於長跨距的拱橋和斜張橋而言，最大的共振反應將發生在列車車速分別為0.88Lf2 和 0.5Lf4 的時候。因此，減少橋樑的振動和增加列車行駛的舒適性，列車車速應適當的選擇以避免車橋共振。

在一般情況下列車車速低於土壤的雷利波速，但如果列車行駛通過一軟弱的土層上，則列車車速將有可能超過土壤的雷利波速，此時將會產生非常大的地表振動。本研究將使用三維有限元素法模擬分析這類型的問題。另外並研究兩種有效的隔振方式，包括設置地下水平混凝土隔振版及土壤改良強固軟弱土壤。最後本文的目標是研究結構基礎大底版對於振動隔絕的效果，所以將進行一個動力的現地量測實驗去研究這個問題。實驗的結果顯示，結構的大底能明顯地隔絕水平方向的振動，但是對於垂直方向的振動隔絕效果有限。

The bridge vibrates when a high-speed train passes. Thus, how to reduce the vibrations induced by high-speed trains is an important issue. In this thesis, a simple finite element model of the moving wheels and cars was developed to simulate the moving high-speed train problems. Then, a three-dimensional finite element method was used to analyze the relationship of resonance between train speed and bridge. The bridge types include multi-simply supported bridge, arch bridge and cable-stayed bridge. According to the finite element results, the resonance is one of the important factors to the bridge vibration. To avoid train-bridge resonance for multi-simply supported bridges, the first dominated train frequency and the first bridge natural frequency in each direction should be as different as possible. If the two first frequencies are similar, the bridge resonance will be very serious. For arch and cable-stayed bridges with long spans, the resonance will produce the maximum response when the train velocity equals 0.88Lf2 and 0.5Lf4, respectively. Thus, the train velocity should be appropriately chosen to avoid train and bridge resonance.

The train speed is generally lower than the Rayleigh speed of soil. If the train moves on a soft ground, its speed may exceed the soil Rayleigh speed, and it may produce large ground vibration. This study used the three-dimensional finite element method to simulate this problem. Additionally, two efficient schemes of the vibration isolation were studied, including the construction of the concrete slab and soil improvement. This thesis aims to find how the building foundation affects the vibration reduction; therefore, dynamic field experiments were performed to investigate this topic. The result of the experiment shows that the foundation slab can significantly reduce the horizontal vibration transformed from soil. But for the vibration isolation of the vertical direction, the reduction is limited.

CONTENTS

ACKNOWLEDGEMENTS (Chinese)	Ⅰ
ABSTRACT (Chinese)	        Ⅱ
ABSTRACT	                Ⅲ
CONTENTS	                IV
LIST OF FIGURES	                X
LIST OF TABLES	                XVII
NOTATIONS	                XVIII

CHAPTER 1 INTRODUCTION	                                              1
1  Background	                                                      1
2  Objectives and Scope of Research	                              2
3  Organization of Dissertation	                              4
  
CHAPTER 2 LITERATURE REVIEW	                                      6
1  Introduction	                                              6
2  Classical Theory of Moving Load Problem	                      6
2.1  Experiment on Real Bridges	                              7
2.2  Theory Research	                                              7
3  Recently Years Theory of Vehicle-Bridge Interaction   	      10
4  The Present Situation of Vehicle-Bridge Vibration Research	      12
5  Wave Propagation of Vibration Induced by Moving Vehicles	      16
6  Isolation of The Vibration of Caused by Moving Vehicles	      18
 
CHAPTER 3 NUMERICAL SCHEMES USED IN THESIS                            21
1  Newmark Direct Integration Method	                              21
2  Newton-Raphson Iteration	                                      24
3  Absorbing Boundary Condition	                              26
4  The Least-Squares Method	                                      26
4.1  Least-Squares Method for Dynamic Equations	              27
4.2  Selecting An Appropriate Harmonic Applied Force  	      30
5  1/3 Octave Band Method	                                      31
6  Fourier Transform (FT) and Fast Fourier Transform (FFT)	      35
6.1  Introduction	                                              35
6.2  Discretely Sampled Data	                                      36
6.3  Discrete Fourier Transform	                              36
6.4  Fast Fourier Transform (FFT)	                              37
7  Numerical Integration	                                      39

CHAPTER 4 FINITE ELEMENT FORMULATION AND RESONANT CHARACTERISTICS 
          OF TRAIN-BRIDGE INTERACTION                                 41
1  Dynamic Equation	                                              41
2  Rayleigh Damping (Proportional Damping)	                      43
3  Finite Element Model of Vehicles	                              45
3.1  Linear-Form Wheel Elements	                              45
3.2  Comparisons Between Analytic and Linear-Form Wheel Elements    47
3.3  Cubic-Form Wheel Elements	                              48
3.4  Comparisons Between Analytic and Cubic-Form Wheel Elements     52
3.5  Modeling The High-Speed Train by Using Wheel element           54
3.6  More accurate model for Moving Train	                      54
3.6.1  Spring-Damper and Lumped Mass Elements	                      55
3.6.2  Rigid Link Effect	                                      55
3.6.3  Vehicle Model Using The Finite Element Schemes	              57
3.7  Validation of The Finite Element Model by Fryba Solution	      60
4  Resonant Characteristics of Train-Bridge Interaction	      65
4.1  Dominated Frequencies of Moving Trains	                      65
4.2  Dominated Frequencies Due to Bridge Length and Train Velocity  67

CHAPTER 5 RESONANCE CHARACTERISTICS OF HIGH-SPEED TRAINS PASSING 
          SIMPLY SUPPORTED BRIDGES	                              71
1  Introduction	                                              71
2  Three-Dimensional Finite Element Analyses of Bridges	      71
3  Finite Element Results and Resonant Characteristics	      75
3.1  Vibration Reduction by The Railway Longitudinal Stiffness 
       Between Simple Beams	                                      76
3.2  Three-Direction Resonant Characteristics of Simply Supported 
       Bridges                                                	      81
3.3  Characteristics of The High-Speed Train Dominated Frequencies  81
4  Summary	                                                      84

CHAPTER 6 NUMERICAL INVESTIGATION OF A STEEL ARCH BRIDGE AND INTERACTION 
          WITH HIGH-SPEED TRAINS	                              85
1  Introduction	                                              85
2  Three-Dimensional Finite Element Analyses of Steel Arch Bridges  85
3  Resonant Characteristics of The Arch Bridge and The Trains	      88
4  Summary	                                                      94

CHAPTER 7 VIBRATION RESPONSES OF CABLE-STAYED BRIDGES UNDER MOVING 
          TRAINS	                                              95
1  Introduction	                                              95
2  Three-Dimensional Finite Element Analyses of Cable-Stayed 
     Bridges                                                          95
3  Characteristics of Train-Induced Bridge Vibration From Finite 
     Element Analyses	                                              98
3.1  Effect of Dominated Frequencies of Trainload	              98
3.2  Relationship Between Impact Factor and Train Speed	      100
4  Summary	                                                      107

CHAPTER 8 THREE-DIMENSIONAL ANALYSES OF TWO HIGH-SPEED TRAINS CROSSING 
          ON A BRIDGE                                        	      108
1  Introduction	                                              108
2  Three-Dimensional Finite Element Analyses of Bridges     	      108
3  Finite Element Results and Dynamic Characteristics	              113
4  Summary	                                                      122

CHAPTER 9 ANALYSIS AND REDUCTION OF TRAIN-INDUCED VIBRATION BELOW 
          AND ABOVE CRITICAL SPEEDS BY FINITE ELEMENT METHOD	      123
1  Introduction	                                              123
2  The Ground Vibrations Due to A Moving Surface Load	              123
2.1  A Moving Load in Soil Dynamics With The Damping Effect	      124
2.2  Numerical Studies of The Vertical Response Induced by A 
       Moving Load With Subsonic Speed	                              131
3  Finite Element Model of High-Speed Train Moving on The Ground    134
3.1  Problem Illustration	                                      134
3.2  Illustration of Finite Element Analysis	                      135
4  Comparison Between Theoretical and Finite Element Solutions      136
5  Finite Element Results Without Isolation Schemes	              140
6  Isolation Effect of Concrete Slab and Soil Improvement	      145
7  Conclusions	                                              149

CHAPTER 10 NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF THE WAVE 
           REDUCTION DUE TO FOUNDATION SLABS	                      150
1  Introduction	                                              150
2  Numerical Study of Wave Reduction Due to Foundation Slab	      151
2.1  Problem Illustration	                                      151
2.2  Illustration of Finite Element Analysis	                      153
2.3  Numerical Results	                                      154
3  Vibration Measurement and Equipment	                      161
3.1  Introduction of Experiment Equipment	                      161
3.1.1  Data Recording and Analysis Equipment	                      161
3.1.2  Vibration Meters	                                      162
3.1.3  Vibration Generator (Shaker)	                              165
3.2  Field Measurements	                                      167
3.2.1  Introduction of Experimental Field and Building (Luchu Base
          and Standard factory building)	                      167
3.2.2  The Setup and Layout of Velocity Meter	              171
3.2.3  The Step of Field Test	                              172
3.3  Results of Field Measurements and Analyses of Test Data	      174
4  Conclusions	                                              181

CHAPTER 11  CONCLUSIONS AND RECOMMENDATIONS                           182                  
1  Conclusions	                                              182
2  Recommendations for Further Research	                      184

REFERENCES	                                                      185
APPENDIX A	                                                      195
APPENDIX B	                                                      197
APPENDIX C	                                                      203
自述	                                                            208
                                    

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