Please wait a minute...
J4  2014, Vol. 48 Issue (2): 228-235    DOI: 10.3785/j.issn.1008-973X.2014.02.007
土木工程     
轨道结构动力响应Newmark方法时间积分步长的确定
史吏1, 蔡袁强1,2, 徐长节1
1.浙江大学 软弱土与环境土工教育部重点实验室,浙江 杭州 310027;2.温州大学 建筑工程学院,浙江 温州 325035
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
 全文: PDF(1942 KB)   HTML
摘要:

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.

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.

出版日期: 2014-02-01
:  TU 45  
基金资助:

国家杰出青年科学基金项目(51025827);国家自然科学基金资助项目(51108414);教育部博士点基金项目(20110101120034)

通讯作者: 蔡袁强, 男, 教授, 博导.     E-mail: caiyq@zju.edu.cn
作者简介: 史吏(1987—), 男, 博士生, 从事土动力学数值计算研究. E-mail:418194187@qq.com
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  

引用本文:

史吏, 蔡袁强, 徐长节. 轨道结构动力响应Newmark方法时间积分步长的确定[J]. J4, 2014, 48(2): 228-235.

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.

链接本文:

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

[1] MEIROVITCH L. Analysis method in vibrations [M]. London: MacMillan, 1967: 102-105.
[2] XU Y L, LI Q, WU D J, et al. Stress and acceleration analysis of coupled vehicle and long-span bridge systems using the mode superposition method [J]. Engineering Structures, 2010, 32: 1356-1368.
[3] RIEKER J R, LIN Y H, TRETHEWEY M W. Discretization conderations in moving load finite element beam models [J]. Finite Elements in Analysis and Design, 1996, 21: 129-144.
[4] OLSSON M. On the fundamental moving load problem [J]. Journal of Sound and Vibration, 1991, 145(2): 299-307.
[5] WU J J, WHITTAKER A R, CARTMELL M P. The use of finite element techniques for calculating the dynamic response of structures to moving loads [J]. Computers & Strucuters, 2000, 78: 789-799.
[6] LIN Y H, TRETHWEY M W. Finite element analysis of elastic beams subjected to moving dynamic load [J]. Journal of Sound and Vibration, 1990, 136(2): 323342.
[7] HENCHI K, FAFARD M, TALBOT M, et al. An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach [J]. Journal of Sound and Vibration, 1998, 212(4): 663-683.
[8] THAMBIRATNAM D, ZHUGE Y. Dynamic analysis of beams on an elastic foundation subjected to moving loads [J]. Journal of Sound and Vibration, 1996, 198(2): 149-169.
[9] JU S H, LIN H T, HSUEH C C, et al. A simple finite element model for vibration analysis induced by moving vehicles [J]. International Journal for Numerical Methods in Engineering, 2006, 68: 1232-1256.
[10] JAFARI A A, EFTEKHARI S A. A new mixed finite element differential quadrature formulation for forced vibration of beams carrying moving loads [J]. Journal of Applied Mechanics, 2011, 78: 1-16.
[11] 李有法.数值计算方法[M].北京:高等教育出版社,1996: 56-58.
[12] 翟婉明.车辆-轨道耦合动力学[M].3版.北京:科学出版社,2007: 72-75.
[13] ZHAI W M, WANG K Y, LIN J H. Modeling and experiment of railway ballast vibrations [J]. Journal of Sound and Vibration, 2004, 270: 673-683.
[14] 蔡袁强,王玉,曹志刚,等.列车运行时由轨道不平顺引起的地基振动研究[J].岩土力学,2012, 33(2): 327-335.
CAI Yuan-qiang, WANG Yu, CAO Zhi-gang, et al. Study of ground vibration from trains caused by track irregularities [J]. Rock and Soil Mechanics, 2012, 33(2): 327-335.
[15] TAKEMIYA H, BIAN X C. Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage [J]. Journal of Engineering Mechanics, 2005, 131: 699-711.
[16] AUERSCH L. The excitation of ground vibration by rail traffic: theory of vehicle-track-soil interaction and measurements on high-speed lines [J]. Journal of Sound and Vibration, 2005, 284: 103-132.

[1] 贾义鹏,吕庆,尚岳全,杜丽丽,支墨墨. 基于粗糙集-理想点法的岩爆预测[J]. J4, 2014, 48(3): 498-503.