{"title":"Analytical solutions for the natural frequencies of rectangular symmetric angle-ply laminated plates","authors":"F. Browning, H. Askes","doi":"10.2140/MEMOCS.2019.7.51","DOIUrl":null,"url":null,"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.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Mechanics of Complex Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/MEMOCS.2019.7.51","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
