端点系有集中质量的弹性杆振动问题  

Oscillation problem on elastic rob with central mass on end

作　　者：程利青[1] 

机构地区：[1]福州大学电子科学与应用物理系,福建福州350002

出　　处：《福州大学学报（自然科学版）》2000年第5期32-37,共6页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省教委基金资助项目!(JB980 0 7)

摘　　要：端点系有集中质量的弹性杆的振动问题的边条件不是斯特姆 -刘维本征值问题所要求的边条件 ,函数系 {Xn(x) }不是正交函数系 ,求解十分困难 .通过提出一种变换 ,将其边条件化为第 1类、第 2类或第 3类边条件 ,此时 {Xn(x) }为正交完备函数系 ,问题大为简化 .最后给出了几种不同的端点情况下的此类问题的解 .It's very difficult to solve the oscillation problem of elastic rob with central mass on end because the boundary condition in this case is not the one required by Sturm-livouville eigen value and the functions {X\-n(x)} are not orthogonal ones. This paper simplifies the problem by presenting a transformation, with which the boundary condition is changed to the boundary condition of first class, second class or third class and then the functions {X\-n(x)} are orthogonal complete functions. Some solutions to such problems with different ends are discussed in this paper.

关 键 词：边界条件 本征值问题 固有频率 弹性杆振动 

分 类 号：TB123[理学—工程力学]