Diffraction of Harmonic Shear Waves on an Elliptical Cavity Located in a Viscoelastic Medium
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 integral Boltzmann–Volterra hereditary relation. The problem of a dynamic stress-s...
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| Veröffentlicht in: | Russian mathematics 2023-08, Vol.67 (8), p.44-48 |
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| container_title | Russian mathematics |
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| creator | Teshaev, M. Kh Karimov, I. M. Umarov, A. O. Zhuraev, Sh. I. |
| description | 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 integral Boltzmann–Volterra hereditary relation. The problem of a dynamic stress-strain state around an elliptical cavity in an unbounded viscoelastic medium under the action of harmonic shear waves is reduced to a plane problem (plane deformation) 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. |
| doi_str_mv | 10.3103/S1066369X23080108 |
| format | Article |
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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.</description><identifier>ISSN: 1066-369X</identifier><identifier>EISSN: 1934-810X</identifier><identifier>DOI: 10.3103/S1066369X23080108</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Cylindrical waves ; Deformation ; Incidence angle ; Incident waves ; Lame functions ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Mathieu function ; Shear ; Transverse waves ; Viscoelasticity ; Wave diffraction</subject><ispartof>Russian mathematics, 2023-08, Vol.67 (8), p.44-48</ispartof><rights>Allerton Press, Inc. 2023. ISSN 1066-369X, Russian Mathematics, 2023, Vol. 67, No. 8, pp. 44–48. © Allerton Press, Inc., 2023. Russian Text © The Author(s), 2023, published in Izvestiya Vysshikh Uchebnykh Zavedenii. 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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.</description><subject>Cylindrical waves</subject><subject>Deformation</subject><subject>Incidence angle</subject><subject>Incident waves</subject><subject>Lame functions</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathieu function</subject><subject>Shear</subject><subject>Transverse waves</subject><subject>Viscoelasticity</subject><subject>Wave diffraction</subject><issn>1066-369X</issn><issn>1934-810X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9Whek7mzlFpboeKiProQhkyS0ZTppCbTQv-9KRVciKt74DvnXDgIXVJyzSnhN3NKpOSyXDBOgFACR2hASy4yoGRxnHTC2Z6forMYl4Tkkgk5QO93rmmC0r3zHfYNnqqw8p3TeP5pVcBvamsjTkh1eNy2bt07rVo8UlvX7_DMa9Vbg13i-NVF7W2rYrLgR2vcZnWOThrVRnvxc4fo5X78PJpms6fJw-h2lmkmoc-41sCAc6IslJLbhqla1iAKKmRR5MIQXpRARA7SQM3rojRAc2MgbwpgueBDdHXoXQf_tbGxr5Z-E7r0smJQCkKpSP1DRA8uHXyMwTbVOriVCruKkmo_YvVnxJRhh0xM3u7Dht_m_0PfzC5yEA</recordid><startdate>20230801</startdate><enddate>20230801</enddate><creator>Teshaev, M. 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| subjects | Cylindrical waves Deformation Incidence angle Incident waves Lame functions Mathematical analysis Mathematics Mathematics and Statistics Mathieu function Shear Transverse waves Viscoelasticity Wave diffraction |
| title | Diffraction of Harmonic Shear Waves on an Elliptical Cavity Located in a Viscoelastic Medium |
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