点杆弹性碰撞问题的一种差分解

A Finite Difference Method for Point Elastic Impact

质点与杆弹性碰撞问题经过若干假设,转化为含碰撞质点作为具有初始速度的附加质量的系统振动问题,这样撞击力可作为内力处理。对所建立的无量纲偏微分方程模型,用差分法求解。边界条件中含有与基本方程同阶次的偏导数项,利用中心差分格式和向后差分格式,并使差分的误差数量级近似于长度方向或时间方向上步长的平方。最后分析讨论了误差和稳定性。

Based on some assumptions,the impact problem between particles and a rod is transformed into a system vibration problem.The system includes the impacting mass with initial velocity.The impact force can be treated as the internal force.For the non-dimensional partial differential model,the finite difference method is used.The boundary conditions include the partial derivation item with the same order of the vibration equation.Using central and backward difference formation,the error＇s order of magnitude is approximated as the square of the displacement or time step.The error and stability are analyzed and discussed.The numerical examples verified the feasibility of the method.