基于杆弹性撞击问题的级数和

本文引入如下力学问题:等截面杆受到具有一定初速度的质点的撞击引起杆的纵向振动.根据已有文献中由DMSM方法得到的响应解,把它代回初始无量纲速度为1的已知条件,得到满足约束方程的变量的级数和,结论以数学形式表达.附录给出用符号软件验证所得结论的程序,其步骤是先求出特征根,再代入级数和表达式进行验证.

Sum of series based on elastic impact problems of rods

This paper introduced the following mechanical problem: a rod was impacted by a particle with a certain velocity. After substituting the solutions, obtained by Direct Mode Shape Superposition Method (DMSM) available in the literatures, into the known condition that the initial non-dimensional velocity was equal to 1, the sum of the series, whose variable satisfied a certain constraining equation, was obtained. The conclusion was expressed in mathematical form. In the appendix, the programs were presented to test the conclusions obtained by using symbol computation software. The first step of the programs was to calculate the eigenvalues, and then substituted the values into the left side of the equations, which verified the correctness of the conclusions.