组合L型变截面梁的自由振动特性分析

Analysis of free vibration characteristics of composite L-shaped variable cross-section beam

组合梁结构常作为大型复杂结构的子机构被广泛应用于机械、土木等设备中。针对组合梁的振动特性问题,提出了一种基于组合L型变截面梁结构振动特性的计算方法。基于欧拉-伯努利梁理论,推导了悬臂L型变截面梁固有频率和振型的计算过程并给出算例。针对计算结果进行了收敛性分析,通过与有限元法对比验证了该方法的有效性。该方法可以为机械或建筑中的框架结构,尤其是有截面变化情况下的动力学计算提供理论基础。

Composite beam structure is often used as a sub-mechanism of large and complex structures and is widely applied in machinery, civil engineering and other equipment. Here, aiming at vibration characteristics problem of composite beam, a calculation method based on vibration characteristics of composite L-shaped variable cross-section beam was proposed. Based on Euler-Bernoulli beam theory, the calculation process of natural frequencies and vibration modes of a cantilever L-shaped variable cross-section beam was deduced, and an example was given. The convergence of the calculation results was analyzed, and the effectiveness of the proposed method was verified by comparing the calculation results obtained using the proposed method with those obtained using the finite element method. It was shown that the proposed method can provide a theoretical basis for dynamic calculation of frame structures in machinery or buildings, especially, in the case of variable cross-section.