Transverse Vibrations of Beams, Exact Versus Approximate Solutions
Transverse Vibrations of Beams, Exact Versus Approximate Solutions
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DOI：
10.1115/1.3157757
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发表时间：
1981-12
期刊：
影响因子：
--
通讯作者：
J. R. Hutchinson
中科院分区：
文献类型：
--
作者：
J. R. Hutchinson
本文求出了有限长度自由-自由圆弧梁固有振动频率的精确解，并与近似解进行了比较。这个精确解是一般线性弹性方程的一个级数解，它收敛于正确的固有频率。通过与以往实验的比较，确定了频率的正确性。用Pochhammer-Chree近似、Timoshenko光束近似和Pickett近似比较了精确解和近似解。比较清楚地表明了近似方法的适用范围和精度。对Timoshenko梁近似中使用的正确剪切系数进行了研究，得出了与前人不同但又补充的结论。
An exact solution for the natural frequencies of vibration of a finite length free-free beam with a circular cross section is found and compared to approximate solutions. This exact solution is a series solution of the general linear elasticity equations which converges to correct natural frequencies. Correctness of the frequencies is established by comparison to previous experiments. Comparison of the exact to approximate solutions is made with the Pochhammer-Chree approximation, the Timoshenko beam approximation and the Pickett approximation. The comparisons clearly show the range of applicability of the approximate methods as well as their accuracy. The correct shear coefficient for use in the Timoshenko beam approximation is investigated and conclusions which differ with, yet at the same time complement, those of previous researchers are reached.