# 臺灣博碩士論文加值系統

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 大眾捷運系統為我們帶來更便捷的交通，但是其伴隨而來之振動問題卻是一個重要的課題。在早期的有限元素研究文獻中，多是著重在二維模型的探討。在此，使用三維模型來進行有限元素分析。使用solid元素來表示土壤及橋樑之上部結構（橋之大樑）。橋支柱及帽梁使用三維梁元素來模擬之。邊界條件為吸收邊界，可用來消除沿著有限元素邊界的反射波，並採用1/3倍頻法來計算振動。本研究分析之步驟和結果，可提供給研究捷運振動問題者一個分析步驟並給予捷運結構系統上舒適與安全性的建議。　　本文有三個主要的案例：1.台北捷運木柵線振動分析。2.台北捷運內湖線振動分析。3.使用全區域三維元素振動分析。在分析結果中，橋樑之振動在列車速度超過70km/hr時，會變的相當明顯，此時頻率為約1.6-1.7Hz。此為車橋共振所造成現象。降低車速至60km/hr以下或是增加橋柱直徑至2.4m可以減少此共振現象。箱型（BOX）結構之橋樑有較小之振動。房屋之大底版可以阻隔來自於基礎土壤之振動，此乃因為底版之水平勁度可以減少同平面的振動。若共振發生時，房屋結構之振動會顯著的增加，此狀況可在本文之有限元素分析中可看出。
 The mass rapid transit system provides us a swift communication, but the vibration problem is always an important issue. Most early finite element investigations were emphasizing of two-dimensional models.　　This investigation uses three-dimensional models to process the finite element analysis. The solid element is used to represent the soil and bridge superstructure (bridge girder). Pillars and pier caps are simulated using three-dimensional beam elements. The absorbing boundaries are used to remove the wave reflection along the finite element boundary. The 1/3 octave band method is adopted to compute the velocity vibration. The analysis procedures and results can provide an analytic process for others vibration investigation and advices about the safety and comfort of metropolitan mass rapid transit system.　　There are three major cases. 1: vibration analysis of Mucha line of Taipei Mass Rapid Transit (TMRT). 2: vibration analysis of Neihu line of TMRT. 3: use macrocosm 3D model to analyze vibration affection. From this investigation, the bridge vibration is obviously (at frequency is 1.6-1.7Hz) when the train velocity is higher than 70km/hr. This phenomenon caused by train-bridge resonance. Decrease the train velocity to 60km/hr or increase the pillar diameter to 2.4m can avoid the resonance phenomenon. The box section bridge has lower vibration. The building bottom slab can isolate the vibration transferred from the foundation soil because the slab horizontal stiffness reduces the in-plane vibration. If the resonance occurs, the building vibration can increase significantly, and this condition can be found in the finite element analysis of this thesis.
 ABSTRACT I摘要 II誌謝 IIICONTENTS IVLIST OF TABLES VIILIST OF FIGURES VIIICHAPTER 1. INTRODUCTION 11.1 Background and purpose 11.2 Literature review 11.3 Brief account of the research 41.4 Illustrate of the finite element program 5CHAPTER 2. NUMERICL SCHEMES USED IN THESIS 102.1 Absorbing boundary 102.2 Wheel elements 112.3 1/3 octave band method 132.4 The least-squares method 162.4.1 Least-squares method for dynamic equations 162.4.2 Selecting an appropriate harmonic applied force 192.5 Newmark direct integration method 21CHAPTER 3. MESH GENERATION PROGRAM OF THE VEHICLE-BRIDGE-SOIL MODEL 243.1 Mesh Generation Program MRTS 243.1.1 Element classification 253.1.2 Input data of program MRTS 293.1.3 Examples 323.1.4 Illustration of the mesh generation program MRTS 333.1.5 Execute program MRTS 373.2 Establish Ground Mesh by VASJAPAN 383.2.1 The required files 393.2.2 Execute program VASJAPAN 453.3 Calculate vibration velocity as program DB 453.3.1 Execute program DB 46CHAPTER 4. MUCHA LINE VIBRATION ANALYSIS 474.1 Bridge system of MuCha line 474.1.1 Establish bridge mesh of MuCha line 564.2 The train finite element model of MuCha line 584.3 The foundation model of MuCha line 594.4 Analysis results of MuCha line 634.5 Discussion 66CHAPTER 5. NEIHU LINE VIBRATION ANALYSIS 675.1 Bridge system of NeiHu line 675.1.1 Establish the bridge finite element model of NeiHu line 715.2 The train finite element model of NeiHu line 745.3 The foundation finite element model of NeiHu 745.4 Example of generate foundation mesh 795.5 Compute the equivalent MCK (mass, damping and stiffness) matrices of NeiHu 855.6 Analysis of NeiHu line 865.6.1 Selecting a suitable bottom node 865.6.2 Analysis results 895.7 Discussion 108CHAPTER 6. NEIHU LINE MACROCOSM 3D FINITE ELEMENT VIBRATION ANALYSIS 1106.1 Building finite element model 1106.1.1 Establish of building mesh 1136.2 Bridge and foundation finite element models 1146.2.1 Bridge mesh 1146.2.2 Ground mesh 1156.3 Macrocosm model 1176.4 Analysis results 1196.5 Discussion 130CHAPTER 7. CONCLUSIONS AND FUTURE WORK 1327.1 Conclusions 1327.2 Future works 133REFERENCE 134