Identifying all combinations of boundary conditions for in-plane vibration of isotropic and anisotropic rectangular plates
Identifying all combinations of boundary conditions for in-plane vibration of isotropic and anisotropic rectangular plates
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DOI：
10.1016/j.tws.2020.107320
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发表时间：
2021-07
影响因子：
6.4
通讯作者：
Y. Narita;M. Innami
中科院分区：
文献类型：
--
作者：
Y. Narita;M. Innami
本文提出了一种有效的振动分析和计数理论的综合研究，以确定各向同性，特别是正交各向异性和对称层合矩形板的面内振动的边界条件的所有组合。首先，本文提出了一种分析方法，可以求出自由、夹紧和两种简支的任意面内边界条件下板的面内固有频率，这种方法可以计算256（=4乘4）组边界条件下矩形板的频率。其次，引入Polya计数理论，从理论上确定板边界条件的不同组合的总数，并将256组简化为基本相同的频率子集。在数值试验中，计算了不同长宽比、不同材料性质和不同层合方式的矩形板的各阶固有频率，并将其按频率相同的类别进行分类。因此，不同的组合获得的板的面内振动，它表明，从实验中的组合的数量完全符合预测的Polya计数理论。
This work presents a combined study of an effective vibration analysis and a counting theory to identify all combinations of boundary conditions for in-plane vibration of isotropic, specially orthotropic and symmetrically laminated rectangular plates. First, a method of analysis is proposed to obtain the in-plane natural frequencies of plates under any in-plane boundary conditions of free, clamp and two types of simple supports, and this method makes it possible to calculate the frequencies of rectangular plates subject to 256(=4 powered by 4) sets of boundary conditions. Secondly, Polya counting theory is introduced to determine theoretically the total number of distinct combinations of plate boundary conditions, and to reduce the 256 sets into the essentially identical subsets of frequencies. In numerical experiments, all sets of natural frequencies are calculated for the rectangular plates with different aspect ratio, material property and lamination, and are sorted into the classes with identical sets of frequencies. The distinct combinations are thus obtained for in-plane vibration of the plates, and it is shown that the number of combinations from the experiment exactly agrees with prediction by Polya counting theory.