高速列车引起地基振动分数阶模型

周星德;吴利平;曾 鹏;韩婷婷;林荣庚

振动与冲击 ›› 2014, Vol. 33 ›› Issue (10) : 34-37.

PDF(1136 KB)
PDF(1136 KB)
振动与冲击 ›› 2014, Vol. 33 ›› Issue (10) : 34-37.
论文

高速列车引起地基振动分数阶模型

  • 周星德,吴利平,曾 鹏,韩婷婷,林荣庚

作者信息 +

A fractional derivative model to train-induced ground vibration

  • ZHOU Xing-de,WU Li-ping,ZENG Peng,HAN Ting-ting,LIN Rong-geng
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摘要

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。

Abstract

A fractional derivative model is developed for predicting ground vibrations from high-speed trains. In order to determine the order of fractional derivative of each soil layer, on the premise of the maximum strain of the ground are <3% and the strain linearly change as time approximately, a linear strain hypothesis is put forward. The function of damping with fractional derivative is proposed by simulating the Binghamton model. The order of fractional derivative of each soil layer can be obtained by using Riemann-Liouville fractional derivative and curve fitting. Considering it is complex and difficult to calculate when the different fractional order existed in motion equations, a generalized damping energy is defined in order to acquire a equivalent order of fractional derivative. In the last, the Sweden’s X2000 high-speed passenger train is taken as the object, the feasibility of the proposed method is demonstrated by comparing with the experimental data.


关键词

高速列车 / 分数阶 / Riemann-Liouville / 阻尼等效 / Oustaloup算法

Key words

high-speed train / fractional order / Riemann-Liouville / equivalent order / Oustaloup method

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周星德;吴利平;曾 鹏;韩婷婷;林荣庚. 高速列车引起地基振动分数阶模型[J]. 振动与冲击, 2014, 33(10): 34-37
ZHOU Xing-de;WU Li-ping;ZENG Peng;HAN Ting-ting;LIN Rong-geng. A fractional derivative model to train-induced ground vibration[J]. Journal of Vibration and Shock, 2014, 33(10): 34-37

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