{"title":"Dynamics of a nanotube supported on the lateral and rotational restrained using doublet mechanics theory","authors":"Murat Akpınar, Büşra Uzun, Mustafa Özgür Yaylı","doi":"10.1007/s00707-024-04173-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, the vibration behavior of a carbon nanotube on an elastic foundation and supported by deformable springs is investigated. In order to include small-size effects in the solution of the problem, the doublet mechanics theory, an atomistic model, is preferred. Since deformable springs are at the ends, the lateral deflection function is proposed in three different regions, using constant coefficients at the boundaries and a Fourier sine series in the region. Then the Stokes' transform is applied to force the boundary conditions into the desired form. After the mathematical arrangements, an eigenvalue problem including small-size effects, elastic foundation effect, and deformable springs is derived. The accuracy of the model is checked by comparing the results obtained with the results obtained in the literature. After receiving a good match with the literature, the effects of various parameters on the vibration frequencies are analyzed on a series of graphical figures and tables.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"809 - 836"},"PeriodicalIF":2.3000,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04173-w","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, the vibration behavior of a carbon nanotube on an elastic foundation and supported by deformable springs is investigated. In order to include small-size effects in the solution of the problem, the doublet mechanics theory, an atomistic model, is preferred. Since deformable springs are at the ends, the lateral deflection function is proposed in three different regions, using constant coefficients at the boundaries and a Fourier sine series in the region. Then the Stokes' transform is applied to force the boundary conditions into the desired form. After the mathematical arrangements, an eigenvalue problem including small-size effects, elastic foundation effect, and deformable springs is derived. The accuracy of the model is checked by comparing the results obtained with the results obtained in the literature. After receiving a good match with the literature, the effects of various parameters on the vibration frequencies are analyzed on a series of graphical figures and tables.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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