Analytic analysis of free vibration problem of the plate with a rectangular cutout using symplectic superposition method combined with domain decomposition technique
{"title":"Analytic analysis of free vibration problem of the plate with a rectangular cutout using symplectic superposition method combined with domain decomposition technique","authors":"","doi":"10.1016/j.enganabound.2024.105890","DOIUrl":null,"url":null,"abstract":"<div><p>Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724003643","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.