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浙江大学学报(工学版)
J4  2014, Vol. 48 Issue (2): 228-235    DOI: 10.3785/j.issn.1008-973X.2014.02.007
    
Time step length determination of Newmark method for dynamic responses of railway tracks
SHI Li1, CAI Yuan-qiang1,2, XU Chang-jie1
1.Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University,
Hangzhou 310027; 2.College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035
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Abstract  

To determine the time step length in calculating dynamic responses of railway tracks by using the Newmark method, a track model consisting of a rail beam on two layers of discrete supports was studied analytically to obtain the amplitude spectrums of the rail-sleeper dynamic reaction forces for a single point load moving at different velocities. Subsequently, the track model was discretized spatially by mode superposition method and the temporal solutions of the resulting equations were obtained by the Newmark method using different time step length. By comparing the temporal results with those obtained by the highly accurate Runge-Kutta integration method, it is found that the time step length of the Newmark method should satisfy the Nyquist theorem. And the frequency band in the Nyquist theorem should be wide enough to include at least the first two valleys of the amplitude spectrum of the rail-sleeper dynamic interaction force, which are contributed by the moving load periodically passing through the discrete supports. As an example, a track model consisting of a rail beam on three layers of discrete supports was studied to obtain the sleeper and the ballast accelerations by the Newmark method with the time step length being determined by the Nyquist theorem.

Published: 01 February 2014
CLC:  TU 45  
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Cite this article:

SHI Li, CAI Yuan-qiang, XU Chang-jie. Time step length determination of Newmark method for dynamic responses of railway tracks. J4, 2014, 48(2): 228-235.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2014.02.007     OR     http://www.zjujournals.com/eng/Y2014/V48/I2/228


轨道结构动力响应Newmark方法时间积分步长的确定

为了明确轨道结构动力响应计算中Newmark方法时间积分步长的确定依据,采用双层离散点支承轨道结构模型解析求解不同移动速度点荷载作用下的轨枕动反力频谱,进而采用模态叠加法和Newmark方法求解不同时间积分步长下上述双层轨道结构的位移和加速度响应,并与高精度的四阶Runge-Kutta方法计算结果对比.结果表明，不同荷载移动速度下的时间积分步长均应满足Nyquist采样定理,且采样定理中的频带宽度应至少包括由离散支承参数激励引起的轨枕动反力频谱的前二阶谷值.作为算例,根据上述采样定理确定的时间积分步长,采用Newmark方法计算了移动列车轴荷载作用下三层离散点支承轨道的枕木及道砟加速度响应.

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