两端固定的Timoshenko梁

The solution of the Timoshenko beam with two fixed ends

Timoshenko梁是目前较为流行的柔性结构梁模型之一.文中研究了两端固定的Timoshenko梁方程解的结构,这是研究Timoshenko梁闭环系统的稳定性及结构的基础性工作.Timoshenko梁方程一般较复杂,很难给出解的解析形式.通过定义系统主算子,将对Timoshenko梁方程的研究转化为对系统主算子的讨论.给出了系统主算子的特征向量的具体解析表达式,完整地描述了Timoshenko梁方程的解的结构,并讨论了Timoshenko梁方程解的某种性质.在此基础上,就可以讨论闭环系统的结构及稳定性问题.

The Timoshenko beam is a kind of popular flexible structure beam at present. In this paper, the solution of the Timoshenko beam with two fixed ends is studied, which is the basis of studying the stability and the structure of the closed loop. Since the equation of the Timoshenko beam is very complex, the analytic form of its solution is difficult to give. In this paper, by defining the main operator of the system, the study of the Timoshenko beam equation is transformed into discussing the main operator of the system. The specific form of the eigenvectors of the main operator is given, so that the solution of the Timoshenko beam is completely described. Moreover, some properties of the solution of the Timoshenko beam with two fixed ends are given. A further discussion of the stability of the closed loop can be conducted based on this paper.