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 本文探討高速列車在不同車速下與土壤之影響。經由理論推導利用數值分析求得其數值解，再透過三維有限元素法模擬高速列車行車振動比較之。 在理論解部份，乃模擬一移動載重在半無限土層中所產生的振動。本研究所探討的是軟弱土壤。車輛行駛在軟弱土層的時，較容易達到發生共振之臨界波速。有限元素法分析全區域之三維模型，分為三個步驟：第一、建立整體系統模型，包含橋樑、列車以及土壤模型。在此土壤方面設定為一均質(homogenous)土層。第二、利用有限元素法分析列車行經之振動反應，包括橋樑、地面之震動。第三、將歷時分析之結果轉至頻率域並以DB (decibel)表示。 由數值分析可知，當車行速度接近土壤雷利波速時，必會產生一極大的瞬間變位。同理我們比較有限元素分析，觀察此一現象是否存在。然而在有限元素分析中，當列車速接近土壤雷利波速時，列車跟土壤並未產生一明顯的共振行為。當列車運行在橋樑上的時候，其所造成的振動，皆會被橋樑系統所分散，對土層影響反而較少。因此對於高鐵振動分析來說，列車-橋樑共振的危害性遠大於列車-土壤共振。垂直變位大部份由列車-橋樑共振所影響，對結構物來說列車-土壤共振幾乎可以忽略。所以在考慮高鐵系統安全性時，設計車輛跟橋樑的自然振動頻率不同，能有效的避免結構共振的發生。 關鍵字: 橋樑、三維有限元素法、1/3倍頻法、高速鐵路、共振、雷利波、振動
 When high-speed trains pass a bridge, there are normally accompanied with increased transient movements of the ground. How to avoid resonance and reduce the vibrations of ground surface induced by a moving load with different speeds has become an important issue. The numerical analysis and the three-dimensional finite element analysis were used in this research to investigate surface ground vibration due to a moving train. This 3D finite element mesh includes the soil and bridge meshes modeled by using the 3D 8-node element. After FEM analysis, 1/3 octave band method was used in frequency domain to compute the vibration from the ground velocity in time domain. The resonant vibration in this study can be clearly seen from the finite element result. As an illustration of the numerical analysis, the train speed v approaches the Rayleigh wave velocity in supporting soil; a large peak has been occurred in the figure approaching track-soil critical velocities. However, it does not have a large increase in generated ground vibrations in the bridge-train-soil model simulated by the finite element method. The vehicle-bridge resonance triggers the greater part of vibrations than the vehicle-soil resonance for the three-dimensional vehicle-bridge-soil system. To be valid for avoid bridge and train resonance, the first dominated train frequency and the first bridge natural frequency in each direction should be as different as possible. Keywords: 1/3 octave band, 3D FEM, Bridge, High-speed train, Resonance, Rayleigh-wave, Vibration.
 CONTENTS 摘要 I ABSTRACT Ⅱ 誌謝 III CONTENTS IV LIST OF TABLES Ⅶ LIST OF FIGURES Ⅷ CHAPTER 1. INTRODUCTION 1 1.1 Background and purpose 1 1.2 Brief account of the research 2 1.3 Literature review 3 1.4 Illustrate of the finite element program 5 CHAPTER 2. THE THEORIES USED IN FEM ANALYSIS 10 2.1 Absorbing boundary 10 2.2 Wheel element 14 2.31/3 octave band method 16 2.4 Newmark direct integration method 17 CHAPTER 3. THEORETICAL BACKGROUND 21 3.1 The description of moving-load problem on an elastic half-space21 3.2 Solution of the basic equations 21 3.3 Subsonic speed 26 3.4 transonic speed 29 CHAPTER 4. ANALYSIS ILLUSTRATIONS AND RESULTS 33 4.1 Numerical study and observations 33 4.2 Compare the displacement with the different locations 36 4.3 Discussion 40 CHAPTER 5. MESH GENERATION PROGRAM OF THE BRIDGE SYSTEM AND FINITE ELEMENT MODEL41 5.1 Establish Ground Mesh by VASJAPAN 41 5.2 The required files 42 5.3 Execute program VASJAPAN 47 5.4 The vehicle-bridge-soil system 47 5.5 Illustration of finite element model 49 CHAPTER 6. FINITE ELEMENT ANALYSIS 57 6.1 Illustrate the generation of bridge foundation mesh 57 6.2 Calculate vibration velocity as program G. 62 6.3 Execute program G 63 6.4 Compare the displacement with the different velocity 64 6.5 Discussion 84 CHAPTER 7. DISCUSSION AND CONCLUSION 86 7.1 DISCUSSION AND CONCLUSION 86 REFERENCES 89 APPENDIX A. Trapezoidal rules for double integrals 92