筒中筒高层结构自由振动的变分解

The Variational Equation for Solving Natural Vibration of Tube in Tube Structure

本文严格证明了按等代筒体法推导出来的筒中筒高层结构自由振动方程是四阶Sturm-Liouville微分方程。用变分法推导出该结构的固有频率计算公式。计算表明,本文方法不仅能求得满意的结果,而且手算过程也十分简单,同时计算结果与模型试验值也符合较好。

In this paper, the equation for solving free vibrations of tube in tube tall building, which is developed by using equivalent closed tube method, is proved strictly to be the fourth-order Sturm-Liouville differential equation, and a formula for calculating natural frequencies of the structure is derived by variational method, In comparison with other three methods for determining the frequencies, the results show that the proposed method is quite satisfactory for practical use and simple in calculation. A good agreement has also been found between the model experimental results and the calculated ones.