{"title":"Oscillations of Nanofilms in a Fluid","authors":"M. A. Ilgamov","doi":"10.1134/s1995080224602212","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Oscillations and waves in a nanofilm in contact with a gaseous medium are considered. It is assumed that the excitation frequencies are in the ultrasonic range. The simplest model is constructed, based on Timoshenko theory of plate bending and on the first approximation of the reaction from the gaseous medium. This takes into account the surface effect caused by the difference in elastic characteristics in the near-surface layer and in the main volume of the material. The derived relations within the Timoshenko model are simplified, which makes it possible to obtain visible results. The contribution of surface effects and reactions from the gaseous medium is assessed. Linear dynamics of a semi-infinite film is studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602212","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Oscillations and waves in a nanofilm in contact with a gaseous medium are considered. It is assumed that the excitation frequencies are in the ultrasonic range. The simplest model is constructed, based on Timoshenko theory of plate bending and on the first approximation of the reaction from the gaseous medium. This takes into account the surface effect caused by the difference in elastic characteristics in the near-surface layer and in the main volume of the material. The derived relations within the Timoshenko model are simplified, which makes it possible to obtain visible results. The contribution of surface effects and reactions from the gaseous medium is assessed. Linear dynamics of a semi-infinite film is studied.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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