Abstract:
We study small-amplitude longitudinal and torsional shock waves in circular cylinders consisting of an anisotropic medium such that the velocities of the longitudinal and torsional waves are close to each other. Previously, simple waves were considered in the same situation and conditions were found for these waves to overturn and for the corresponding shock waves to form. Here we present the study of shock waves: the shock adiabat and the evolutionary conditions. The results obtained can also be related to shock waves in unbounded media with quadratic nonlinearity.
Citation:
A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 109–122; Proc. Steklov Inst. Math., 300 (2018), 100–113
\Bibitem{KulChu18}
\by A.~G.~Kulikovskii, A.~P.~Chugainova
\paper Shock waves in anisotropic cylinders
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 109--122
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3860}
\crossref{https://doi.org/10.1134/S0371968518010089}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 300
\pages 100--113
\crossref{https://doi.org/10.1134/S008154381801008X}
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Linking options:
https://www.mathnet.ru/eng/tm3860
https://doi.org/10.1134/S0371968518010089
https://www.mathnet.ru/eng/tm/v300/p109
This publication is cited in the following 4 articles:
A. G. Kulikovskii, A. P. Chugainova, “Longitudinal–Torsional Waves in Nonlinear Elastic Rods”, Proc. Steklov Inst. Math., 322 (2023), 151–160
A. G. Kulikovskii, A. P. Chugainova, “Structures of non-classical discontinuities in solutions of hyperbolic systems of equations”, Russian Math. Surveys, 77:1 (2022), 47–79
A. G. Kulikovskii, A. P. Chugainova, “Discontinuity Structures of Solutions to Equations Describing Longitudinal–Torsional Waves in Elastic Rods”, Dokl. Phys., 66:4 (2021), 110
A. P. Chugainova, A. G. Kulikovskii, “Longitudinal and torsional shock waves in anisotropic elastic cylinders”, Z. Angew. Math. Phys., 71:1 (2020), 17
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