基于有限差分法的水平旋转梁自由振动解析

Free vibration analysis of horizontal spinning beams by using finite difference method

在水平旋转梁模型的基础上,利用哈密尔顿原理建立了动力学微分方程。在悬臂梁边界条件下,运用二阶中心差分原理对欧拉梁进行有限差分离散,推导出系统模型的自由振动差分方程。运用MATLAB振动工具箱和一般阻尼振动理论对其进行了编程运算,得到了不同转速下水平梁的无量纲固有频率。相关文献的结果比对验证了有限差分方法的有效性,然后对旋转梁的自由振动特性进行了扩展分析和结果的优化处理。另外,对固支梁和自由梁的自由振动也进行了解析。

Dynamic differential equations were built according to Hamiltonian principle for a horizontal spinning beam. The cantilever beam was discretized by second-order central differences, and difference equations of free vibration were developed. A MATLAB vibration toolbox program and the general damped vibration theory were introduced to derive the dimensionless natural frequencies at different rotational speeds. The finite difference method was proved effective by comparing the results with those in other references, and free vibration characteristics of spinning uniform beams were analysed and optimized. Numerical analysis of free vibration characteristics was also made on free-free and clamped- clamped beams.