基于精细Runge-Kutta混合积分法的车桥耦合振动非迭代求解算法

杜宪亭 夏禾 张田 田园 曹艳梅

振动与冲击 ›› 2013, Vol. 32 ›› Issue (13) : 39-42.

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (13) : 39-42.
论文

基于精细Runge-Kutta混合积分法的车桥耦合振动非迭代求解算法

  • 杜宪亭 夏禾 张田 田园 曹艳梅
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NON-ITERATIVE SOLVING ALGORITHM OF TRAIN-BRIDGE SYSTEM BASED ON PRECISE RUNGE-KUTTA HYBRID INTEGRATION METHOD

  • Du Xian-ting, Xia He, Zhang Tian, Tian Yuan, Cao Yan-mei
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摘要

针对结构非线性问题,采用4阶Runge-Kutta法展开精细积分法中响应状态方程的Duhamel项,构造了一种既可以避免迭代又具有较高精度的精细Runge-Kutta混合积分方法,在此基础上提出了适用于车桥耦合振动高效求解的分析框架。车桥耦合系统由车辆、桥梁子系统组成,均采用有限元建模,其中车辆子系统采用部件刚体假定,而桥梁子系统借助于振型叠加法缩减自由度数目;两个子系统内部非线性作用以及系统间的相互作用通过非线性的虚拟力表达。以一节4轴客车匀速通过32m简支梁为研究对象,分别采用分析框架法、Runge-Kutta法进行动力分析。数值结果对比表明:相对于Runge-Kutta法,精细Runge-Kutta混合法能够显著提高计算收敛的积分步长;分析框架可以应用到实际工程中。

Abstract

A precise Runge-Kutta hybrid integration method with high accuracy is constructed to solve structural nonlinear problems without iteration, in which the Duhamel term of state equation of the precise integration method is expanded in terms of 4-order Runge-Kutta method. Based on the method, an efficient analysis framework for dynamic interaction analysis of train-bridge system is proposed. The train-bridge system consists of a train subsystem and a bridge subsystem, and both subsystems are established by using finite element method. The rigid component assumption is introduced to the train subsystem, while the mode superposition method is applied to the bridge subsystem to reduce the number of degree-of-freedom. The inner nonlinear effect of both subsystems and the dynamic interaction between two subsystems are taken as virtual forces. A 4-axle vehicle passing through the simply supported beam with 32m span at constant speed is taken as a case study. The dynamic analysis of the coupled system is carried out by using the proposed framework and the Runge-Kutta method. The comparison of numerical results shows that the convergent time interval of precise Runge-Kutta hybrid integration method may be greatly larger than that of Runge-Kutta method, and that the proposed framework may be expanded in practice.

关键词

车桥系统 / 动力相互作用 / 精细积分法 / Runge-Kutta法 / 振型叠加法

Key words

train-bridge system / dynamic interaction / precise integration method / Runge-Kutta method / mode superposition method

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杜宪亭 夏禾 张田 田园 曹艳梅. 基于精细Runge-Kutta混合积分法的车桥耦合振动非迭代求解算法[J]. 振动与冲击, 2013, 32(13): 39-42
Du Xian-ting;Xia He;Zhang Tian;Tian Yuan;Cao Yan-mei. NON-ITERATIVE SOLVING ALGORITHM OF TRAIN-BRIDGE SYSTEM BASED ON PRECISE RUNGE-KUTTA HYBRID INTEGRATION METHOD[J]. Journal of Vibration and Shock, 2013, 32(13): 39-42

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