{"title":"Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane","authors":"M.A. Lyalinov","doi":"10.1134/S1061920824030105","DOIUrl":null,"url":null,"abstract":"<p> The paper deals with the formal short-wavelength asymptotic solutions describing the acoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, and covered by a thin elastic membrane. The solutions are localized in the medium near the line of the rigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in the asymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas the frequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-type condition. </p><p> <b> DOI</b> 10.1134/S1061920824030105 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"477 - 494"},"PeriodicalIF":1.7000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824030105","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The paper deals with the formal short-wavelength asymptotic solutions describing the acoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, and covered by a thin elastic membrane. The solutions are localized in the medium near the line of the rigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in the asymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas the frequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-type condition.
本文论述了描述一个具有坚硬底部、由声学介质填充并由薄弹性膜覆盖的容器中声学特征振荡的形式短波长渐近解。这些解都集中在覆盖容器的薄膜与容器边缘刚性接触线附近的介质中。解的渐近展开中的系数满足可解问题的重复序列，而存在这种非微不足道的形式解的频率则服从渐近 "量子化类型条件"。 doi 10.1134/s1061920824030105
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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