由纵向振动引起的质点与圆锥形杆碰撞问题的解析解

Analytical Solutions for Response of Collision of Particle With Conical Rod Caused by Longitudinal Vibration

给出细长圆锥形的截面杆受到质点纵向碰撞时的精确解析解.提出了一种新方法用于分析质点_圆锥形杆碰撞,使用了叠加法给出杆的响应.其结果可验证数值解和其他解析解.所提出方法的优点之一是响应解的解析形式简洁.结论是质量比和一些描述杆几何形状的变量,如倾斜度、杆长和半径在撞击分析中具有重要作用.

The objective is to present analytical solutions of longitudinal impact analysis for slender conical rods struck by a particle and a new method is proposed for conical rod-particle impact analysis, in which the superposition method is used and the response of the rod is presented. These analytical results are exact and can be used to validate the numerical methods or other analytical results. The numerical example shows that one of the advantages of the present method is that the analytical form is very simple. The result is that mass ratio and some variables describing the geometrical shape of rods such as taper, length and radius play an important role in impact dynamic system.