中文摘要：

基于波传播法对球与细长圆锥杆纵向碰撞动力学问题进行研究.建立了考虑非线性弹性接触变形的球与圆锥杆纵向碰撞的动力学方程,通过引入分段求解的思想,提出了球与圆锥杆碰撞动力学方程的求解算法.通过对钢球与铝圆锥杆低速碰撞问题进行数值仿真,讨论了不同锥度和质量比等因素对碰撞力和动力学响应的影响,研究了不同锥度条件下应变波传播性质,为今后实验和数值研究提供了理论参考.研究结果表明：圆锥杆锥度和质量比等参数对碰撞力和圆锥杆上速度响应作用明显;由截面不等引起的锥度对应变波传播造成的影响不可忽视.

英文摘要：

Based on the wave propagation method the impact dynamics of a sphere colliding with a slender conical rod was investigated. The impact dynamic equations with considering nonlinear elastic contact deformation were established. Through sub-solving techniques, the solution algorithm was presented. The numerical examples of the impact between the steel sphere and the aluminum conical rod were simulated. The effects of the taper of the conical rod and mass ratio of the rod on the sphere were discussed, and the propagation properties of strain wave were studied under the condition of the different taper. The theory reference was provided for the numerical simulation and the experimental research. The results indicate that the impact force and velocity response of the system are greatly influenced by the taper and the mass ratio, and the effects of the taper in the strain wave propagation can not be ignored.