高层框架自由振动的Sturm-Liouville微分方程

The Sturm-Liouville equation for free vibration of framed-structures

提出一个计算高层框架基本周期的简单方法.为简化计算,用一个等直弯-剪悬臂梁来模拟高层框架结构进行动力分析.证明了高层框架自由振动的微分方程是四阶Sturm-Liouville微分方程,用变分法推导出计算高层框架自由振动基本周期的表达式.

A simple method for calculating fundamental period of framed structures is described in this paper. To simplify their computation, a uniform shear- flexure cantilever beam model is used to perform a dynamic analysis of framed structure. To present a simple technique for the calculation, a resulting equation for free vibration of the structure is proved strictly to be forth - order Sturm - Liouville differential equation, and a formulation for calculating fundamental natural period of the structure is derived. An engineering example is worked out in detail to illustrate that the method provides result that compares closely with it obtained from the usual method of analysis.