# 臺灣博碩士論文加值系統

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 本文為研究橋樑雙向高速會車之三維結構之動力特性分析。以每垮30m共有十個跨距的簡支梁橋，按照實際的車橋參數來做有限元素法之動力分析。本文中使用了一反應比為雙向列車與單向列車對橋樑振動反應之比值。由有限元素法之分析結果指出當兩列車車速近乎相同時，其反應比其值在垂直方向明顯增加，其最大值接近但小於兩倍。此結果顯示出雙向交會車之最大振動反應近乎為單向列車之兩倍。而當雙向列車之車速有很大差異時，則反應比一般皆接近一，這意謂雙向會車之動力影響是接近於單向列車。同時，有限元素結果亦指出當雙向會車車速相同時，平均反應比之值在三個大域方向為1.65。
 This thesis investigates the dynamic characteristics of the three-dimensional vehicle-bridge system when two high-speed trains in crossing on the bridges. Multi-span bridges with high piers and simply supported beams were used in the dynamic finite element analysis. A comparison ratio was defined in this study to represent the ratio of the vehicle-bridge response of two-way trains to that of one-way train. Finite element results indicate that the comparison ratio increases significantly when two-way trains run near the same speed, and the maximum comparison ratio is approximately equal to but smaller than two for the vertical dynamic response. This means that the maximum dynamic response of the two-way trains is at most twice of the one-way train dynamic response. When the two-way train speeds are sufficiently different, the comparison ratio approaches one averagely, which means that the dynamic effect of the two-way train is similar to that of the one-way train. Finite element results also indicate that the averaged comparison ratio in the three global directions is about 1.65 when the two-way trains run with the same speed.
 CONTENTSABSTRACT…………………………………………………………………I摘要 ⅡAcknowledgements………………………………………….......................IIICONTENTS………………………………………………………………...IVLIST OF FIGURES VILIST OF TABLES ⅥICHAPTER 1. INTRODUCTION 1 1.1 Background and purpose 1 1.2 Brief account of the research 3 1.3 Literature review 4CHAPTER 2. FINITE ELEMENT FORMULATION 6 2.1 Dynamic equations 6 2.2 Formulation of the Newmark direct integration method 10 2.3 THEORY OF 3D BEAM ELEMENT WITH RIGID ZONE EFFECT 142.4 Rayleigh Damping………………………………………………….…19CHAPTER 3. FINITE ELEMENT MODEL OF VEHICLES 20 3.1 Introduction 20 3.2 Finite element model of vehicles 203.3 3D finite element analyses of bridges 24CHAPTER 4. RESONANCE CHARACTERISTICS OF HIGH SPEED TRAINS PASSING SIMPLY SUPPORTED BRIDGES 30 4.1 Introduction 30 4.2 DOMINATED FREQUENCY OF MOVING TRAINS 30 4.3Three-direction vibration characteristics of simple supported bridge………………………………………………………………….31CHAPTER 5. Finite element results and dynamic characteristics 37 5.1 Time History Example Of The Bridge’s Displacement Subjected To The Pass Of Two-Way Trains 37 5.2 Finite element results and dynamic characteristics 38REFERENCES 51List of figuresFigure pageFigure 2-1 Moments and shears in axes 2-3 15Figure 2-2 Moments and shears in axes 3-1 15Figure 3-1 Mass and dimensions of the modified SKS-700 high-speed train 26Figure 3-2 Moving wheel element 26Figure 3-3 Sprung mass moving on a simple beam 26Figure 3-4 Comparisons between analytic (Biggs, 1964) and finite element solutions for the simple beam subjected to a moving sprung mass ………………….………………...27Figure 3-5 Finite element model and dimensions of the bridge……………………………...28Figure 3-6 The direction of high-speed trains in crossing on the simply supported bridge …29Figure 4-1 Frequency response of the three global direction axial force at the 6th pier changing with the train velocity from 220 to 490km/h (right-way trains) ………….35Figure 4-2 Frequency response of the three global direction axial force at the 6th pier changing with the train velocity from 220 to 490km/h (left-way trains) 36Figure 5-1 Time history of the bridge’s displacement subjected to the pass of two-way trains …..47Figure 5-2 Response ratio of the X shear force at the 4th to 7th pier changing with the train velocity from 220 to 490km/h 48Figure 5-3 Response ratio of the Y shear force at th*e 4th to 7th pier changing with the train velocity from 220 to 490km/h 49Figure 5-4 Response ratio of the Z axial force at the 4th to 7th pier changing with the train velocity from 220 to 490km/h 50List of tablesTables PageTable 2.1 Step-by-step solution using Newmark integration method 12Table 2.2 Step-by-step solution using Newmark integration method using Rayleigh damping 13Table 4-1. First-mode bridge natural frequencies in the three global directions 34
 References1.Biggs, J.M. (1964), Introduction to Structural Dynamics, McGraw-Hill, Inc., New York.2.Cheng, Y.S., Au, F.T.K., and Cheung, Y.K. (2001), “Vibration of railway bridges under a moving train by using bridge-track-vehicle element”, Eng. Struct., 23(12), 1597-1606.3.Ju, S.-H. (2002), “Finite element analyses of wave propagations due to high-speed train across bridges”. Accepted by Int. J. Num. Meth. Eng.4.Klasztorny, M. (2001), “Vertical vibration of a multi-span beam steel bridge induced by a superfast passenger train”, Struct. Eng. Mech., 12(3), 267-281.5.Li, J.-Z., and Su, M.-B. (1999), “The resonant vibration for a simply supported girder bridge under high-speed trains”, J. Sound Vib., 224(5), 897-915.6.Tang, C.-C. and Wang, Y.-C. (2002), “Dynamic characteristics of elastic beams subjected to traffic loads”,Struct. Eng. Mech., 13(2), 211-230.7.Xia, H., Xu, Y.-L., and Chan, T.-H.-T. (2000), “Dynamic interaction of long suspension bridges with running trains”, J. Sound Vib., 237(2), 263-280.8.Yang, Y.-B., and Lin, B.-H. (1995), “Vehicle-bridge interaction analysis by dynamic condensation method”, J. Struct. Eng., ASCE, 121(11), 1636-1643.9.Yang, Y.-B., Yau, J.-D., and Hsu, L.-C. (1997), “Vibration of simple beams due to trains moving at high speed”, Eng. Struct., 19(11), 936-944.10.Zhang, Q.-L., Vrouwenvelder, A., and Wardenier, J. (2001), “Numerical simulation of train-bridge interactive dynamics”, Comput. Struct., 79(10), 1059-1075.11.Ju, S.H. 2001. Finite element analyses of wave propagations due to high-speed train across bridges. Accepted by International Journal for Numerical Methods in Engineering.
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 1 捷運系統高架橋行車振動分析 2 三維殼元素於有限元素法之架構 3 格巢式振波納消塊之有限元素分析 4 三維非線性樑元素用於結構分析之研究 5 非彈性結構大變形動態分析之平行計算 6 土中障礙物對振波阻隔之試驗研究 7 瀝青混凝土車轍過程中粗粒料之行為分析 8 軌道列車排點模式與求解方法 9 捷運列車引致土層振動與衰減特性之研究 10 FWD動態分析及探討反算修正因子 11 微構件剖面對蜂巢材料雙軸抗壓行為之影響 12 井孔中鑽管受自重及軸力之挫屈分析 13 液流阻尼器全尺寸結構防振功能之振動台測試 14 微結構缺陷對蜂巢材料疲勞壽命之影響 15 決策優選比較分析法評估既有鋼筋混凝土橋樑之損傷等級

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