Higher-order theory for bending and vibration of beams with circular cross section
Higher-order theory for bending and vibration of beams with circular cross section
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DOI：
10.1007/s10665-013-9620-2
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发表时间：
2013-02
影响因子：
1.3
通讯作者：
Y. Huang;J. Wu;X. Li;L. Yang
中科院分区：
文献类型：
--
作者：
Y. Huang;J. Wu;X. Li;L. Yang
本文提出了一种分析同时考虑转动惯量和剪切变形的圆形截面圆柱梁自由振动的高效、简便的高阶理论。与Timoshenko梁理论不同，本方法不需要剪切修正系数。类似于矩形梁的Levinson理论，该新模型是圆形截面梁的高阶理论。对于这类圆柱梁的横向弯曲，基于圆柱体圆周面上的无牵引力条件，首先推导出挠度和转角的两个耦合控制方程，然后将其组合成一个控制方程。在截面没有翘曲的情况下，我们的结果是准确的。与Timoshenko梁理论、Euler-Bernoulli梁理论和有限元方法的固有频率进行了比较。我们的结果对准确理解圆柱梁的力学行为和工程设计是有用的。
This paper presents an efficient and simple higher-order theory for analyzing free vibration of cylindrical beams with circular cross section where the rotary inertia and shear deformation are taken into account simultaneously. Unlike the Timoshenko theory of beams, the present method does not require a shear correction factor. Similar to the Levinson theory for rectangular beams, this new model is a higher-order theory for beams with circular cross section. For transverse flexure of such cylindrical beams, based on the traction-free condition at the circumferential surface of the cylinder, two coupled governing equations for the deflection and rotation angle are first derived and then combined to yield a single governing equation. In the case of no warping of the cross section, our results are exact. A comparison is made of the natural frequencies with those using the Timoshenko and Euler–Bernoulli theories of beams and the finite element method. Our results are useful for precisely understanding the mechanical behavior and engineering design of circular cylindrical beams.