高速列车引起地基振动分数阶模型

A fractional derivative model for highspeed train-induced ground vibration

为更准确描述列车道轨地基土体阻尼特征,引入分数阶模型。各层土体分数阶次通过Riemann-Liouville分数阶定义、测试数据,据曲线拟合方式确定;考虑含分数阶运动方程计算复杂,将各土层分数阶次借助阻尼等效原则变为一等效分数阶次;采用Oustaloup算法将分数阶通过频域逼近方式获得整数阶表示。用Matlab软件进行仿真分析,并与实测结果对比。

A fractional derivative model was developed for predicting ground vibrations induced by high-speed trains.In order to determine the order of fractional derivative of each soil layer,on the premise that the maximum strain of ground is less than 3%and the strain approximately linearly changes with time,a linear strain hypothesis was put forward. The damping function with fractional derivative was proposed by simulating Binghamton model.The order of fractional derivative of each soil layer was obtained by using Riemann-Liouville fractional derivative and curve fitting.As the order of fractional derivative was complex and difficult to calculate when different fractional orders existed in equations of motion,a generalized damping energy was defined in order to acquire an equivalent damping order of fractional derivatives.At last, a Sweden＆#39;s X2000 high-speed passenger train was taken as an example,the feasibility of the proposed method was demonstrated by comparing the simulation results with the proposed method with test data.