具有耗散接头的三维欧拉─伯努利杆系的特征频率

Eigenfrequencies of the Three Dimensional Euler-Bernoulli Beam System with Dissipative Joints

本文计算了具有耗散接头的一般非共线的欧拉─伯努利或铁木辛柯杆系结构振动特征频率的传递矩阵．将允许结构是三维的，因此，一定要同时研究各种振动模式，包括纵向和扭转的振动。这种结构一般可以看作是由许多杆件首尾相接构成一条链条。允许有各种不同的减振器，甚至有些减振器是本结构内部形成的．我们也允许在结构中采用不同材料，杆件也可以是不同宽度。本文证明了可以利用渐近估计方法来求得近似的特征频率。

In this paper,we will compute the transfer matrices to find the eigenfre- quencies for the vibrations of the general non-collinear Euler-Bernoulli or Timo- shenko beam structure with dissipative joints.We will allow the structure to be three dimensional,and thus we must consider all types of vibrations simultan- eously.including longitudinal and torsional vibrations.The general structureconsidered will consist of any number of beams joined end to end to form a chain. Many different kinds of dampers are allowed,even within the same structure. We also will allow different materials within the structure as well asdifferent beam widths.We then will show that asymptotic estimates can be usedto find the eigenfrequencies approximately.