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The ray method for solving boundary problems of wave dynamics for bodies having curvilinear anisotropy

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Summary

The ray method for solving boundary problems involving the propagation of surfaces of strong discontinuity in curvilinear anisotropic media is developed. The method employs the solution behind the surface of strong discontinuity which is constructed in terms of power series (ray series). Shock subjections to boundaries of cavities in transversely isotropic bodies having cylindrical, toroidal and spherical anisotropies are investigated. It is demonstrated that in some cases the uniform validity of truncated ray series is not impaired over domains of the wave motion existence. For their improvement, the authors suggest a new method, the method of forward-area regularization, which allows one to extend the truncated ray series over the whole region of the wave solution existence.

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Author notes

  1. Yu. A. Rossikhin & M. V. Shitikova

    Present address: Department of Theoretical Mechanics, Voronezh State Academy of Construction and Architecture, ul. 20-letiya Oktyabrya 84, 394006, Voronezh, Russia

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    1. Yu. A. Rossikhin
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    2. M. V. Shitikova
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    Rossikhin, Y.A., Shitikova, M.V. The ray method for solving boundary problems of wave dynamics for bodies having curvilinear anisotropy. Acta Mechanica 109, 49–64 (1995). https://doi.org/10.1007/BF01176816

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    • DOI: https://doi.org/10.1007/BF01176816

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