Oscillations of Nanofilms in a Fluid

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s1995080224602212

M. A. Ilgamov

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.

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流体中纳米薄膜的振荡

摘要研究考虑了与气体介质接触的纳米薄膜中的振荡和波。假设激励频率在超声波范围内。根据季莫申科板弯曲理论和气体介质反应的第一近似值，建立了最简单的模型。该模型考虑到了近表面层和材料主体积弹性特性不同所造成的表面效应。简化了季莫申科模型中的推导关系，从而可以获得可见的结果。对表面效应和气体介质反应的贡献进行了评估。研究了半无限薄膜的线性动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

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.