彈性支承橋梁於移動載重作用下之動態互制分析

Abstract

本文旨在探討彈性支承橋樑受高速移動列車載重作用下所產生之動態互制效應。為了能更真實的模擬車橋互制的行為，本文將車輛模擬成移動單軸與雙軸系統；橋面部分模擬成軌道不平整及由車輪與軌道系統之合成勁度與阻尼所組成的黏彈性層；橋樑支承部分則模擬成具豎向勁度的彈性支承。 在分析的過程中，首先推導車橋互制運動方程式與橋梁之振態函數，再利用無因次參數及有限傅立葉轉換等技巧，獲得無因次常微分方程組。因此配合無因次初始條件，便可以Runge-Kutta法求得車橋各項函數之數值解。 最後，由實例進行車橋動態互制分析，以探討車橋各項函數於錯車、不同速度參數與橋跨時之歷時反應、最大反應之發生位置，及橋樑支承勁度、車橋各項參數、軌道系統、簡化模型等與最大反應間之關係。

The paper is aimed at the investigation of the dynamic interaction effects for elastic supported bridge under moving loads of high-speed trains. For precisely simulating the vehicle-bridge interaction, we model moving vehicle loads, bridge surface and bridge support in moving one-axle system and moving two-axle system, the visco-elastic layer composed of spring and viscous damping of wheel and ballast track system, as well as elastic support subjected to vertical translation. First, vehicle-bridge interaction motion equation and mode shape of bridge were formulated in process of analysis. Second, we used the skill of dimensionless parameters and finite Fourier transformation to get dimensionless form of a set of ordinary differential equations. After combining with dimensionless form of initial conditions, we can obtain the numerical solution for every function of vehicle-bridge by Runge-Kutta method. At last, we'll use several examples to analyze the vehicle-bridge dynamic interaction, in order to investigate time history response in two vehicle passing each other, different bridge span and velocity parameter, the position of maximum response, as well as the relation between maximum response, stiffness of bridge support, dimensionless parameters, track system, and simplified model, etc.