傳統分析上，常以移動質量或移動力問題來求解，但其分別會高估與低估了動力互制的暫態反應，而且多忽略了軌道結構的影響。軌道系統是一個會隨著車輛與橋樑產生振動的柔性結構，尤其是在高速行駛之下，其對於橋樑與列車間的動力互制效應將會有重要的影響。本研究中，我們暫不考慮襯墊和枕木的效應，而將軌道結構視為一無限長的樑，置於一層道碴基礎上，橋樑結構則為簡支橋樑系統。
我們在本研究中，採用了一個更接近真實車體的多懸浮剛體模型，以進行三維模式的車輛運動模擬。傳統作法常假設僅有一列車，以等速依一定方向行進，而我們則考慮了多種車況的模擬，如，多列車同向行進或兩列車交互穿越等情況，作一比較分析。
對於車輛或橋樑，我們皆可以完全的模擬它們的動力效應。當列車在高速行進時，完整的動力分析才能正確的計算動力互制問題。與傳統的微分方程式相較，我們所使用了積分型式的求解法，它消去了高階的空間微分項、Delta函數和結構的邊界條件。所以，本文使用的方法有容易考慮複雜的結構型式及車輛運行的情況等優點。
在列車運動上，車體的反應是乘客舒適度的一項重要指標，根據我們的結果顯示，高速行駛較低速時有較高的平順度。意即，高速行駛下較為舒適。最後，兩條軌道之間的交互影響效應，其影響函數應更認真的來加以考量，並加入枕木的模擬等。希望本研究在此問題上能有些許的貢獻，也期望往後的發展會有更真實、更理想的成果。

The dynamic response of a bridge structure due to traveling vehicles has long been a subject of intensive research in engineering. In Taiwan, the project of a high-speed railway system in the west corridor between Taipei and Kaohsiung is under construction. A special feature of the Taiwan high-speed railway is that the elevated bridges have been adopted as the major supporting structures for over 70 percent of the railway lines. Thus, the problem of train-bridge interaction has become an important issue.
In the majority of reported studies for the vehicle structure interaction, the basic method of analysis is solving a set of partial differential equation. In the formulation, simplified vehicle models are assumed. For a low-speed railway system, the vehicle can often be represented as a set of concentrated forces, and the track structure on the bridge can be ignored. For high-speed trains, it is necessary to consider the vehicle as a set of mass particles to include the heaving inertia of the train.
The analyses based on simplified vehicle and structural models clearly do not simulate the realistic responses of the system. In this study, we adopted a direct numerical approach. In the model, three sub-system, the vehicle, the bridge structure, and the dynamic interaction, and formulated separately. Compatibility and equilibrium conditions link them together. For the interaction model, an integral equation is used. Neglecting the actions of railpads and sleepers, the track structure can be simplified as an infinite, continuous rail lying on a single-layer ballast foundation and bridge as a simply supported beam. A realistic three-dimensional modeling of the high-speed train by using a set of multiple rigid bodies is also developed. Classical approach often assumes a single train moving at constant speed. In this study, it is possible to consider different combination of train operations, including following trains and trains crossing one another.
The result shows that our approach can be accurate in computing both the vehicle and bridge responses, especially in high speed. In comparison with the traditional partial differential form, the integral formulation eliminates the high-order spatial derivatives, the Delta functions and explicit boundary conditions. Thus, the numerical approach has the advantages of considering complicated vehicle and structural models.
It is interesting to note that if the response of the sprung body has been taken as a measure of the passenger’s riding comfort, our study shows that the vibration period of the train body increases as the traversing speed increases. This indicates that the motion of a high-speed train is smoother than a low-speed one.

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