列车动力学的非线性数值分析方法

Nonlinear Numerical Methods for Train Dynamic Analysis

列车动力学方程是个复杂非线性方程,必须采用数值积分方法求解。本文从工程实用的观点出发,提供了二类简单有效的数值积分方法——Newmark显式积分法及其显-隐式预测-校正积分法。这类积分方法,积分过程简捷,程序编制容易;由于积分过程中无须求解高阶线性代数方程组,这就显著地提高了积分速度,并有效地节约了计算内存,从而在普通微机上实现了对大型列车动力学问题的模拟分析。文中建议了一种判定工程实际问题之非线性数值积分稳定性的实用办法,并成功地应用于重载列车动力学分析。在此基础上进一步实现了变步长积分计算,大大提高了计算速度。通过算例校验及与试验结果的对照,证实了方法的非线性数值分析有效性。

It is difficult to integrate train dynamic equations because of their complicate nonlinear properties. For the sake of simplif- ying the integration process, thus convenient for engineering use, this paper presents two types of numerical integration methods: Newmark's explicit algorithm and its explicit-implicit predictor-corrector algorithm. When using these methods, the solution of high order algebraic linear equations is no longer necessary and the computational time is greatly reduced. So the methods can be applicable to analyse the problems of train dynamics on common micro-computers. In the paper, a criterion is also presented to determine the numerical stability of any integration method solving complex nonlinear problems from engineering practice. Using this criterion to train dynamics, a step-changed integration technique is established to enhance the calculating speed. The accuracy is tested by two nonlinear numerical examples, and by comparing calculated results with actual test data.