Vibrations of a hanging Timoshenko beam under gravity
Vibrations of a hanging Timoshenko beam under gravity
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DOI：
10.1016/0022-460x(90)90838-q
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发表时间：
1990-09
影响因子：
4.7
通讯作者：
T. Yokoyama
中科院分区：
文献类型：
--
作者：
T. Yokoyama
研究了重力作用下均匀悬挂梁的振动特性。首先从哈密顿原理导出了受自重作用的垂直悬垂铁木申科梁自由振动的控制微分方程。然后用有限元程序离散这些方程的空间依赖性。研究了重力、剪切变形和转动惯量对悬挂梁弯曲振动的影响。特别是，得到的经典欧拉-伯努利梁的固有频率和相关振型与已有的实验和数值结果吻合得很好，这是本模型的一个特例。本文的研究结果有助于更好地理解重力作用下大型柔性空间梁的动力特性。
The vibration characteristics of uniform hanging beams under gravity are investigated. The governing differential equations for free vibrations of a vertically hanging Timoshenko beam subjected to its own weight are first derived from Hamilton's principle. The spatial dependence of these equations is then discretized by using a finite element procedure. The influences of gravity, shear deformation and rotatory inertia on the flexural vibrations of the hanging beam are examined. In particular, the natural frequencies and the associated mode shapes obtained for the classical Euler-Bernoulli beam, which is a special case of the present model, show good agreement with the available experimental and numerical results. The present results provide a better understanding of the dynamic characteristics of a large flexible space beam under gravity.