铁道车辆系统周期解的延续算法

用有限差分格式离散常微分方程组的周期解,形成一个含参数的非线性代数方程组,用DERPAR算法对该含参数代数方程组进行延续求解,不但可计算稳定的周期解,而且不稳定的周期解也可求出,采用了van de Pol方程和Lorenz方程验证了该方法的可行性.用上述方法计算了一个17自由度铁路客车模型的周期解,得到了一个大范围的车辆系统周期解的解图,包括稳定的和不稳定的周期解.确定了客车系统Hopf分叉点及系统的非线性临界速度,分析了车辆系统周期和轮对横移幅值与车速的关系.

A PERIODIC SOLUTION OF RAILWAY VEHICLE SYSTEM USING CONTINUATION METHOD

The periodic solution of the ordinary differential equations is discretized using the finite difference method and the nonlinear algebraic equations with a parameter are obtained. The equations are solved continuously using the DERPAR algorithm and the stable and unstable periodic solutions are calculated. The feasibility of the method is verified by calculating the van de Pol equation and Lorenz equations. A railway passenger car model with 17 degrees of freedom is set up and the periodic solutions of the system are obtained. The solution diagram of the vehicle system in a large area is obtained which includes the stable and unstable periodic solutions. The Hopf bifurcation point and the nonlinear critical speed of the vehicle system are determined. The relations of vehicle system period and lateral displacement amplitude of wheelset with respect to the vehicle speed are investigated.