Timoshenko悬臂梁自振特性分析的新方法

考虑剪切变形和转动惯量的影响， 建立了Timoshenko悬臂梁自由振动分析的哈密顿体系，采用两端边值特征值问题的本征值计数精细积分法，求解其圆频率，分析自振特性。本文以等截面欧拉悬臂梁自由振动为基础，本文方法与解析解对比，验证了本文方法的正确性。进而考虑剪切变形和转动惯量的影响，计算了Timoshenko悬臂梁的自振圆频率，分析其自振特性。从算例结果对比可以看出，本文方法简单，实用，具有较高精度。

A new method of free vibration analysis of Timoshenko cantilever beams

Being considered the effect of the shearing and moment of intertia,the Hamilton system of free vibration of the Timoshenko cantilever beams was set up. The circular frequency for the two ends eigenvalue problem was calculated by using the method of precise integration of eigenvalue counting theory. Then the free vibration was analyzed. Based on the free vibration of the uniform Euler beams, The correctness of this method was verified through the calculation result comparison with this method and the traditional method. Then the circular frequency of the Timoshenko cantilever beams with the consideration under the effect of the shearing and the moment of intertia was calculated. The comparison results show that the method is simple,practicable and with good precision.