Timoshenko悬臂梁自由振动特性的近似分析方法

本文讨论了用模态摄动法分析Timoshenko悬臂梁的自由振动特性。Timoshenko梁是目前较为流行的梁模型之一，Timoshenko梁方程一般较复杂，很难给出解的解析形式。利用模态摄动法，将Timoshenko梁方程转化为一组非线性代数方程组的求解，不仅可以简化计算过程，而且计算结果具有较高的精度，对任意边界条件下的Timoshenko梁都适用。通过算例，讨论了剪切变形和转动惯量对悬臂梁的固有频率的影响。

An Approach for Analyzing Free Vibration Characteristics of Timoshenko Cantilever Beams

This paper discussed a method of modal perturbation to analyze the characteristics of free vibration of Timoshenko cantilever beams. The Timoshenko beam is a kind of popular beam at present. Since the equation of the Timoshenko beam is very complex, the analytic form of its solution is obtained difficultly. In this method, the equation of Timoshenko beam can be transferred as a set of nonlinear algebraic equations. This method can predigest the process of calculation and the result of calculation also owns good precision, it is applicable to Timoshenko beams with any arbitrary boundaries. The effect of the shear distortion and the moment of inertia on the natural frequency of Timoshenko cantilever beams is discussed from several numerical examples.