Analytical solutions for the natural frequencies of rectangular symmetric angle-ply laminated plates

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2019-04-22 DOI:10.2140/MEMOCS.2019.7.51

F. Browning, H. Askes

引用次数: 2

Abstract

Analytical solutions, based on the Ritz method, are derived for the lowest natural frequency of rectangular symmetric angle-ply laminated plates. Since symmetric angle-ply plates have nonzero cross-elasticity constants, the solutions are approximate. The accuracy of these solutions is tested with a convergence study using the Rayleigh quotient iteration method. With the solutions available in symbolic form, parameter studies are presented that establish the effect of plate aspect ratio and ply orientation angle for a number of stacking geometries. The results are also verified through a comparison with numerical Ritz solutions, showing a maximum error of 5% in our approximate solution.

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矩形对称角层合板固有频率的解析解

基于里兹法，导出了矩形对称角层合板最低固有频率的解析解。由于对称角层板具有非零的交叉弹性常数，所以解是近似的。通过瑞利商迭代法的收敛性研究，验证了这些解的准确性。利用符号形式的解，给出了参数研究，确定了板长宽比和层向角对若干堆叠几何形状的影响。通过与数值Ritz解的比较验证了结果，表明我们的近似解的最大误差为5%。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.