摘要
对于车辆系统非线性稳态方程Ｆ（Ｘ）＝０的数值求解，一般都是直接采用牛顿迭代法或其各种改进的迭代法，但牛顿法只有局部的收敛性。本文提出一种沿积分曲线下降的方法，根据系统的稳态方法来合理构造一组具有渐近稳定解的常微分方程，使其平衡位置解即为稳态方程的解。通过对该微分方程进行数值积分，可得Ｆ（Ｘ）＝０的近似解。然后，结合牛顿－拉夫森迭代法进行解的精确化。该方法能够保证稳态方程的求解在大范围内具有较好的收敛性。最后，以一构架式转向架货车的稳态曲线通过为计算实例，对其动力性能进行了分析计算。从数值计算结果看，证明所采用的数值分析方法是行之有效的，具有应用价值。
The Newton Iteration or its modified methods are usually employed for solving thevehicle steady state equation F(X)=0,but the Newton method only possesses local convergence. This paper gives an algorithm called descent method along integral curves of ordinary differential equations. The stationary solution of the differential equations are the solution ofthe steady state equations.A approximate solution of equation F(X)=0 can be obtainedthrough numerical integration to the differential equations. Then,the solution can be accurately solved by use of Newton Raphson Iteration. The algorithm established in this papercan ensure good convergence in large region for solving steady state equations. Finally,thesteady state curving of a freight car is taken as a computational example. Its curving behaviour has been calculated and analyzed. From the point of view of the numerical results,the adopted numerical method is proved to be efficient and is of value to the investigation of vehicle steady state curving behaviour.
出处
《铁道学报》
EI
CSCD
北大核心
1994年第A06期125-130,共6页
Journal of the China Railway Society
关键词
车辆
稳态方程
微分方程
收敛解
vehicle system,steady state equation,differential equation,convergent solution,curving
