This paper presents the governing equation of motion, boundary conditions and exact vibration frequencies of a segmented rod where the segments are connected by hinges with elastic rotational springs of constant stiffness. The mass of each segment is assumed to be evenly distributed along the length of the rod. Another discrete model called Hencky bar-chain model (short for HBM; which is equivalent to the finite difference model for discretizing continuous rod) assumes the rod mass to be lumped at the ends instead and a different set of boundary conditions are adopted clamped end. The vibration results of a clamped–clamped segment rod are compared with those of the HBM. It is shown that the HBM underestimates the vibration frequencies when compared to the segmented rod model for a finite number of segments while both models furnish vibration solutions that converge to the solutions of Euler beam for infinitely large number of segments.

中文翻译：

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分段杆的振动

本文介绍了分段杆的运动控制方程、边界条件和精确的振动频率，其中分段通过具有恒定刚度的弹性旋转弹簧的铰链连接。假设每个段的质量沿杆的长度均匀分布。另一个离散模型称为 Hencky bar-chain 模型（HBM 的缩写；相当于离散连续杆的有限差分模型）假设杆质量在端部集中，并采用不同的边界条件集夹紧端部。将夹紧-夹紧节段杆的振动结果与 HBM 的振动结果进行了比较。