{"title":"Free vibration and buckling analysis of simply supported rectangular nano-plates: A closed-form solution based on nonlocal 3D elasticity theory","authors":"Parvaneh Nateghi-Babagi , Bahram Navayi-Neya , Morteza Eskandari-Ghadi","doi":"10.1016/j.ijsolstr.2025.113261","DOIUrl":null,"url":null,"abstract":"<div><div>Free vibration and stability analysis of simply supported rectangular nano-plates is presented based on Eringen’s nonlocal elasticity theory, where an exact solution is proposed to determine natural frequencies and critical buckling loads of nonlocal plates. Accordingly, a set of new scalar potential functions is introduced to decouple either coupled equations of motion or buckling equations. Afterward, the method of separation of variables is utilized to solve PDEs governing potential functions in each case. Followingly, solutions of potential functions and displacements are expressed in the form of double Fourier series. However, the accuracy of the present method is confirmed by comparing the obtained results with the simpler case of molecular dynamic simulation, and other nonlocal methods. It is also noteworthy that this study presents a novel method with high accuracy and precision which facilitates analysis of nano systems. The developed scheme can be useful for vibration and stability analysis of two- and three-dimensional systems in nano dimensions. Small-scale, aspect ratio and thickness ratio effects in vibration and stability analysis are also investigated. Final results demonstrate that the thickness ratio has a significant effect on the vibrational and stability behavior of nanoplates, which is increased by considering non-local relationships in three dimensions.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"312 ","pages":"Article 113261"},"PeriodicalIF":3.8000,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Solids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020768325000472","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/6 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Free vibration and stability analysis of simply supported rectangular nano-plates is presented based on Eringen’s nonlocal elasticity theory, where an exact solution is proposed to determine natural frequencies and critical buckling loads of nonlocal plates. Accordingly, a set of new scalar potential functions is introduced to decouple either coupled equations of motion or buckling equations. Afterward, the method of separation of variables is utilized to solve PDEs governing potential functions in each case. Followingly, solutions of potential functions and displacements are expressed in the form of double Fourier series. However, the accuracy of the present method is confirmed by comparing the obtained results with the simpler case of molecular dynamic simulation, and other nonlocal methods. It is also noteworthy that this study presents a novel method with high accuracy and precision which facilitates analysis of nano systems. The developed scheme can be useful for vibration and stability analysis of two- and three-dimensional systems in nano dimensions. Small-scale, aspect ratio and thickness ratio effects in vibration and stability analysis are also investigated. Final results demonstrate that the thickness ratio has a significant effect on the vibrational and stability behavior of nanoplates, which is increased by considering non-local relationships in three dimensions.
期刊介绍：
The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field.
Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.
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
