端点系有集中质量的串联弹性杆的纵振动

Vibration Problem of Elastic Rod in Series with Concentrated Mass on One End

一端固定,另一端系有集中质量的串联弹性杆的纵振动问题是一种不规范的施图姆-刘维尔本征值问题,用分离变量法求解,得到本征值满足的超越方程,数值计算其本征值,得到串联弹性杆纵振动的级数解,进一步讨论了集中质量质点的振动模式和系统的能量问题.

It is a kind of irregular Sturm-Liouville eigenvalue problem that the vibration of rod in series with concentrated mass on one end, solving the vibration by separation variable to obtain the equation of eiginvalue,which can be solved by numerical method, the series solution of the vibration can be given, then the vibration model of concentrated mass and the engery of system are discussed.