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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 8, Pages 64–70
DOI: https://doi.org/10.26907/0021-3446-2023-8-64-70 (Mi ivm9909) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Diffraction of harmonic shear waves on an elliptical cavity located in a viscoelastic medium

M. Kh. Teshaeva, I. M. Karimovb, A. O. Umarovc, Sh. I. Zhuraevd

a Bukhara Branch of the Institute of Mathematics named after V.I. Romanovskiy at the Academy of sciences of the Republic of Uzbekistan, 11 M. Ikbol str., Bukhara, 200118 Republic of Uzbekistan
b Tashkent Institute of Chemical Technology, 32 A. Navoi str., Tashkent, 100011 Republic of Uzbekistan
c Bukhara Institute of Engineering and Technology, 15 Murtazaev str., Bukhara, 200100 Republic of Uzbekistan
d Bukhara State University, 11 M. Ikbol str., Bukhara, 200118 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2023-8-64-70
Abstract: The problem of diffraction of harmonic shear waves on an elliptical cylindrical cavity located in a viscoelastic medium is considered. The relationship between stresses and deformations is taken into account using the hereditary integral Boltzmann-Voltaire relation. The problem of a dynamic stress-strain state around an elliptical cavity in an unlimited viscoelastic medium under the action of harmonic shear waves is reduced to a plane problem (plane deformable state) of viscoelasticity. The Lame equation reduces to the solution of the Mathieu equation with complex arguments. Its solution is expressed in terms of Mathieu functions. Numerical results are obtained for different frequencies of incident waves, angles of incidence of the transverse wave and the ratio of the axes of the elliptical cavity.
Keywords: shear waves, elliptical cylinder, Mathieu equation, Boltzmann–Voltaire relations, complex argument.
Received: 29.03.2023
Revised: 29.03.2023
Accepted: 29.05.2023
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 8, Pages 44–48
DOI: https://doi.org/10.3103/S1066369X23080108
Document Type: Article
UDC: 517.968
Language: Russian
Citation: M. Kh. Teshaev, I. M. Karimov, A. O. Umarov, Sh. I. Zhuraev, “Diffraction of harmonic shear waves on an elliptical cavity located in a viscoelastic medium”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 8, 64–70; Russian Math. (Iz. VUZ), 67:8 (2023), 44–48
Citation in format AMSBIB
\Bibitem{TesKarUma23}
\by M.~Kh.~Teshaev, I.~M.~Karimov, A.~O.~Umarov, Sh.~I.~Zhuraev
\paper Diffraction of harmonic shear waves on an elliptical cavity located in a viscoelastic medium
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 8
\pages 64--70
\mathnet{http://mi.mathnet.ru/ivm9909}
\crossref{https://doi.org/10.26907/0021-3446-2023-8-64-70}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 8
\pages 44--48
\crossref{https://doi.org/10.3103/S1066369X23080108}
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