变速移动荷载下轨道结构动力响应解析解研究

AN ANALYTICAL SOLUTION FOR RAILWAY TRACK STRUCTURE RESPONSE UNDER MOVING LOADS WITH VARIABLE SPEEDS

为了研究列车进出站对周围环境的振动影响,推导了轨道结构在变速移动荷载作用下动力响应的解析解形式。首先以Duhamel积分为基础,应用动力互等定理,得到了变速移动荷载作用下,半无限弹性空间体上任意点动力响应的一般表达式;然后在该式的基础上,针对轨道结构的周期性特点,将荷载沿钢轨的移动问题转化为拾振点以轨枕间距为周期向反方向跳跃式移动与荷载只在一个轨枕间距内移动的组合问题。以此,将一个频域积分问题转化为了拾振点频域周期解析的叠加问题,从而得到了轨道结构在变速移动荷载作用下动力响应的解析解形式。最后通过对匀速和变速移动荷载作用下轨道结构响应算例的分析和对比,验证了理论的正确性。

In order to study the environmental vibration response due to entering-station and leaving-station trains on their railway, a new dynamic periodic close form solution is introduced for the railway structure subjected to moving loads with variable speeds in this paper. Firstly, the general dynamical response in an elastic half space model subjected to the surface moving loads is obtained on the basis of Duhamel integral and dynamic reciprocity theorem. Secondly, in the case of a periodic railway track structure, the general dynamical response in the frequency domain is simplified in a form of summation within the track sleeper period instead of integral, which is obtained by transferring the moving loads on the rail to the moving of receiver backward within a periodic sleeper distance and the moving of loads within only one sleeper distance. The advantage of this formulation is that all of the dynamical analyses of the track system is carried out within a sleeper distance. In this way, the track response by the moving train can be obtained. Finally, by studying the cases of loads moving on the track structure with variable and constant speeds, the theory has been proved to be correct.