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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 4, Pages 666–683
DOI: https://doi.org/10.31857/S0044466921040098 (Mi zvmmf11229) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Mathematical physics

Anomalies of acoustic wave propagation in two semi-infinite cylinders connected by a flattened ligament

S. A. Nazarova, L. Chesnelb

a Saint Petersburg State University
b 91128 Palaiseau, France, Route de Saclay, INRIA/Centre de mathématiques appliquées, École Polytechnique, Université Paris-Saclay, France
Citations (3)
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DOI: https://doi.org/10.31857/S0044466921040098
Abstract: We study the propagation of waves in a waveguide which is the union of two semi-infinite cylinders connected by a thin rectangular ligament. It is shown that almost complete or even complete transmission of the piston mode at a prescribed frequency can be achieved via fine tuning of the plate sizes, although, of course, almost complete wave reflection occurs in the generic case. The result is obtained by applying an asymptotic analysis of the scattering coefficients of the acoustic wave, in particular, by using the dimension reduction procedure on the thin ligament. Possible generalizations of the problem formulation and related open questions are discussed.
Key words: acoustic waveguide, connecting ligament, asymptotics of scattering coefficients, almost complete reflection and transmission of piston modes.
Funding agency Grant number
Russian Science Foundation 17-11-01003
This work was supported by the Russian Science Foundation, project no. 17-11-01003.
Received: 21.07.2020
Revised: 14.10.2020
Accepted: 16.11.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 4, Pages 646–663
DOI: https://doi.org/10.1134/S0965542521040096
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: S. A. Nazarov, L. Chesnel, “Anomalies of acoustic wave propagation in two semi-infinite cylinders connected by a flattened ligament”, Zh. Vychisl. Mat. Mat. Fiz., 61:4 (2021), 666–683; Comput. Math. Math. Phys., 61:4 (2021), 646–663
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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