Abstract:
We provide a representation of the general solution to the two-dimensional equations of the dynamics of a transverse isotropic medium with the Carrier–Gassmann condition. The representation of the solution is based on two solving functions that satisfy two separate wave equations. The problem of the reflection of plane waves from a rigid wall and a free surface is solved. The reflection coefficients and transformations of plane waves are found. The obtained formulas imply the solution for an isotropic medium as well. Special cases are considered, where the forms (amplitudes) of the reflected waves are not determined uniquely but related to the form of a falling wave through a linear relation.
Keywords:
transverse isotropy, plane wave, Carrier–Gassmann condition, coefficients of reflection and transformation.
Citation:
B. D. Annin, N. I. Ostrosablin, “Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium”, Sib. Zh. Ind. Mat., 19:1 (2016), 27–36; J. Appl. Industr. Math., 10:1 (2016), 29–36
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\by B.~D.~Annin, N.~I.~Ostrosablin
\paper Reflection of plane waves from a~rigid wall and a~free surface in a~transverse isotropic medium
\jour Sib. Zh. Ind. Mat.
\yr 2016
\vol 19
\issue 1
\pages 27--36
\mathnet{http://mi.mathnet.ru/sjim909}
\crossref{https://doi.org/10.17377/sibjim.2016.19.103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549855}
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\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 1
\pages 29--36
\crossref{https://doi.org/10.1134/S199047891601004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961666350}
Linking options:
https://www.mathnet.ru/eng/sjim909
https://www.mathnet.ru/eng/sjim/v19/i1/p27
This publication is cited in the following 2 articles:
B. D. Annin, N. I. Ostrosablin, “Presentation of the general solution of three-dimensional dynamic equations of a transversely isotropic thermoelastic medium”, J. Appl. Mech. Tech. Phys., 60:2 (2019), 224–233
Boris D. Annin, Nikolay I. Ostrosablin, Rostislav I. Ugryumov, AIP Conference Proceedings, 2035, 2018, 050003
Citation in format AMSBIB
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