自從十九世紀以來，列車（Vehicle）、軌道（Rail）與橋樑（Bridge）的動力互制行為一向是一個重要研究的課題，研究結果廣泛應用於橋樑、飛機、跑道以及油管和涵管的安全設計上。在最近的二十年，由於高速鐵路的興建，動力互制行為的問題，在國內也越來越受到注重。 在台灣，在台北和高雄之間的西部走廊，構築一條高速鐵路系統 的計畫已經開始。台灣高速鐵路（HSR）有一個特徵，就是路線的百分之七十以上，採用高架橋樑為主要支承架構。因此，橋樑的互制（Interaction）與振動（Vibration）問題，也有其特別的重要性。 在過去的研究方面，橋樑上的軌道結構常被簡化，列車則模擬成一連串的移動力或移動質量。移動力分析（Moving force analysis）是最簡單的模型，但是它排除了車輛慣性影響的考慮。而移動質量分析（Moving mass analysis）是高速行車時必要的，它正確地考慮了車輛與橋樑間的作用力。但是，若考慮乘客的舒適性與振動對周遭環境的影響，這樣一個簡單的模型仍然不能得到精確的結果。 對於高速列車，一連串的質量質點並不能確切的計算列車的慣性。因此，在我們的研究中，我們考慮較接近真實車體的多懸浮剛體模式（moving multiple-rigidbody model），進行二維車輛運動的模擬。另外，在本文中，我們也考慮了不同結合的列車運作，包括一連串的列車組及二個列車組彼此交互穿越等狀況。 對於動力互制的行為，我們考慮了一個積分方程式來表示互制應有的平衡與諧合條件。因此，本文的方法是將整個系統分為三部分：行車動力系統、軌道與橋樑系統及動力互制行為系統（Dynamic interaction system）。分析的方法主要為差分法，因此，是一個直接的數值分析方法。 The dynamic interactions of train-rail-bridge have been a subject of research since the nineteenth century. In the last twenty years, due to the construction of a high-speed railway system, the problem of train-rail-bridge interactions has received increasing attention in Taiwan. A high-speed railway (HSR) system in the west corridor between Taipei and Kaohsiung has been under construction. One special feature of the Taiwan high-speed railway is that the elevated bridges are adopted as the major supporting structures for over seventy percent of the railway lines.In the previous studies, a train was often modelled as a series of moving forces or moving masses, while the track structure existing on the bridge was ignored. The moving force model is one of the simplest analysis that excludes consideration of the effect of inertia of the vehicle. The moving mass model is an improved one for high-speed trains that accurately describes the force between the structure and the vehicle. But such simplified model is sufficiently accurate, if the riding comfort and environmental vibrations due to the train are of major concern. A series of mass particles do not accurately describe the heaving inertia of the train. Thus, in this study, we consider a more realistic two-dimensional modeling of the high-speed train by using a series of multiple rigid bodies. We also consider different combination of train operations, including a series of following trains and two trains crossing each other.
