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研究生:劉鈞皓
研究生(外文):Jun-Hao Liu
論文名稱:橋樑支承墊阻尼對高鐵行車震動之影響分析
論文名稱(外文):Investigation of Bridge Vibration due to the Damping Ratio Variation in Bearing Plate under High-speed-train Loading
指導教授:朱聖浩
指導教授(外文):Sheng-Hao Zhu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:102
中文關鍵詞:三維網格共振橡膠支承墊有限元素法高架橋振動阻尼比鉛心橡膠支承墊高速鐵路AN 程式
外文關鍵詞:Damping ratioAN programFEMrubber-bearing plateLRBHigh speed trainResonanceThree-dimensional meshViaduct vibration
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高架橋樑系統成為高速鐵路土建結構的主要選擇,因此,近年來探討列車行經橋樑時造成動力的行為是個相當重要的題材。一般來說,地震力作用之下適當阻尼比的支承墊可以明顯的減少橋樑的振動,然而,在微震的情況之下是否也會一樣。另外,對於使用樑元素分析橋樑振動,並探討樑元素與三維元素結果比較的差異性。
本文的主要目的是以有限元素法探討以上所提到的兩個問題。首先,探討當高速列車經過時不同的支承墊阻尼比下的振動位移,結果指出在不同支承墊阻尼比的情況下並不會非常明顯。接著,探討三維樑元素與支承墊情況下的差異,比較結果指出軌道的勁度與支承墊上的摩擦力應該大致上與樑元素模型相同。假使忽略了這兩個影響,兩
者的差異就會非常的大。因此,對於樑元素來說,兩簡支樑之間的勁度假設與支承墊是非常重要的。
The viaduct system has become the main choice for high-speed railways. Thus, investigating the dynamic behavior of bridges caused by the passing vehicles or trains has been an important subject of research recently. Usually, bearing plates with a suitable damping ratio can considerably reduce bridge vibration due to seismic loading. However, it should be a question that the above condition is still valid for micro vibration. To analyze bridge vibration, people usually use beam element to model the bridge for simplification. This, therefore, causes another question what is the analysis difference between the simplified beam model and the precise three-dimensional solid model.
The main purpose of this thesis is to investigate the above two questions using the finite element method. First, the vibration displacement of the bridge for different damping ratios in the bearing plates is investigated during the high-speed train loading. The results indicate that the change of the damping ratio of the bearing plate is not obvious. Second, the bridge was analyzed using the beam model that simulates the bridge using three-dimensional beam elements. The analysis difference between the beam models and three-dimensional solid models was discussed. The comparison indicates that the stiffness of the rail and the friction on the bearing plate should be appropriately modeled for the beam model. If one ignores the two effects that mean the model without rail stiffness and bearing plate friction, the difference can be considerably large for the two models. At this condition, the shear forceof the pier increases significantly in the bridge direction using the beam model. Thus, suitable assumptions between two simply supported beams and bearing plates are very important for the beam model.
ABSTRACT I
摘要 III
誌謝 IV
CONTENTS V
LIST OF TABLES Ⅷ
LIST OF FIGURES IX
CHAPTER 1. INTRODUCTION 1
1.1 Background and purpose of the research 1
1.2 Literature review 2
1.3 Brief account of the research 4
1.4 Illustrate of the finite element program 5
CHAPTER 2. NUMERICAL THEORY USED IN THE THESIS 11
2.1 Absorbing boundary 11
2.2 Wheel element 12
2.3 Newmark direct integration method 15
2.4 Calculation of 1/3 octave band from the finite element result 17
2.5 Illustration of bridge system 19
CHAPTER 3. MESH GENERATION PROGRAM OF THE MODEL 26
3.1 Mesh generation program MRTSBOX 26
3.1.1 Input data of program MRTSBOX 27
3.1.2 Example 28
3.1.3 Illustration of the mesh generation program MRTSBOX 29
3.1.4 The required file to execute program MRTSBOX 33
3.2 The program Gbdall9 32
3.2.1 Summarized account of program Gbdall9 34
3.2.2 Element classification 34
3.2.3 Input data of program Gbdall9 37
3.2.4 Example for beam section 39
3.3 Calculate vibration velocity with program DB 39
CHAPTER 4. THE DISPLACEMENT ANALYSIS OF BRIDGE UNDER DIFFERENT
DAMPING RATIO 49
4.1 The brief introduction of the bearing plate 49
4.1.1 The material characteristic of rubber bearing plate 49
4.1.2 Concerning the lead-rubber bearing plate 50
4.2 Compare the displacement under the different damping ratios 51
4.2.1 The program MMM 51
4.2.2 Compare the displacement of node under the different damping
ratios 52
4.2.3 The displacement of the nodes under different damping ratios 52
4.2.4 Analysis results of LRB 53
4.2.5 Analysis results of rubber bearing plate 55
4.3 Conclusion for the influence of different damping ratio under
the conditions of LRB and rubber bearing plate 57
CHAPTER 5. COMPARISON OF THE DISPLACEMENT WITH BEAM ELEMENT AND
BEARING PLATE 74
5.1 Bridge model of beam finite element established 74
5.2 Bridge structure of beam finite element analysis 74
5.3 Analysis results in the frequency domain 78
5.3.1 Program MMM1 78
5.3.2 Discussion 79
CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 98
6.1 Conclusions 98
6.2 Future works 99
REFERENCES 100
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