Beam and Plate Theories: A New Look at Timoshenko-ehrenfest and Uflyand-mindlin Equations
Beam and Plate Theories: A New Look at Timoshenko-ehrenfest and Uflyand-mindlin Equations
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DOI：
10.1142/10890
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发表时间：
2018-06
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通讯作者：
I. Elishakoff
中科院分区：
文献类型：
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作者：
I. Elishakoff
在本章中，我们将讨论均匀和均质 Timoshenko-Ehrenfest 梁固有频率的精确解。我们首先从横向变形相同消失的情况的最简单解决方案开始。然后，我们一方面由 Majkut (2009) 提供，另一方面由 Cazzani 等人 (2016a, b, c) 提供的一般情况的精确解决方案。还应该提及 Trail-Nash 和 Collar (1953)、Huang (1961a, b) 的论文以及 Karnovsky 和 Lebed (2001) 的书，用于计算各种边界条件 (BC) 下的 Timoshenko-Ehrenfest 梁频率，包括更高模态的模态函数的变化。
In this chapter, we deal with exact solutions for natural frequencies of uniform and homogeneous Timoshenko–Ehrenfest beams. We start first with simplest solution for the case where the transverse deformation vanishes identically. Then we expose exact solutions for the general case provided on one hand by Majkut (2009) and on the other hand by Cazzani et al.(2016a, b, c). One should also mention the papers of Trail-Nash and Collar (1953), Huang (1961a, b), and the book of Karnovsky and Lebed (2001) for the calculation of Timoshenko–Ehrenfest beam frequencies for various boundary conditions (BCs) including the change of modal function for higher modes.