Email this article 
Asymptotic methods for solving boundary value problems for symmetric and antisymmetric hyperbolic boundary layer in shells of revolution in the vicinity of dilatational and shear wave fronts
- Authors: Kirillova I.V.1
-
Affiliations:
- Saratov State University
- Issue: Vol 89, No 6 (2025)
- Pages: 1019-1027
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/364152
- DOI: https://doi.org/10.7868/S3034575825060106
- ID: 364152
Cite item
Open Access
Access granted
Subscription Access
Abstract
Asymptotic methods for solving boundary value problems for three types of hyperbolic boundary layers in the case of shells of revolution of arbitrary profile are developed: symmetric and antisymmetric boundary layers in the vicinity of the dilatation wave front and antisymmetric boundary layers in the vicinity of the shear wave front. The solutions are based on the use of solutions for the hyperbolic boundary layer in the case of a cylindrical shell, that is, on the so-called "basic solutions". The basic solutions are obtained using integral Laplace transforms with respect to time and Fourier transforms with respect to the longitudinal coordinate, followed by expansion of the Laplace images into a series of oscillation modes. Solutions for the general case of shells of revolution also use decompositions of the images into a series of oscillation modes, which are obtained using the exponential representation method. The obtained analytical solution methods fully implement
About the authors
I. V. Kirillova
Saratov State University
Author for correspondence.
Email: iv@sgu.ru
Saratov
References
- Nigul U. Regions of effective application of the methods of three-dimensional and two-dimensional analysis of transient stress waves in shells and plates // International Journal of Solids and Structures, 1969, vol. 5, no. 6, pp. 607–627. http://dx.doi.org/10.1016/0020-7683(69)90031-6
- Goldenveizer A.L. Theory of Thin Elastic Shells. Moscow: Nauka, 1976. 512 p. (in Russian)
- Kossovich L.Y. Nonstationary Problems of the Theory of Thin Elastic Shells. Saratov: Saratov University Press, 1986. 176 p. (in Russian)
- Kaplunov J.D., Nolde E.V., Kossovich L.Y. Dynamics of Thin Walled Elastic Bodies. San Diego: Academic Press, 1998. 226 p.
- Kirillova I.V., Kossovich L.Y. An asymptotic model for the nonstationary waves in the shells of revolution initiated by the LT type edge shock loading // Current Developments in Solid Mechanics and Their Applications. Advanced Structured Materials. Springer Nature Switzerland AG, 2025, vol. 223, pp. 315–342. http://dx.doi.org/10.1007/978-3-031-90022-8_22
- Asymptotic theory of wave processes in thin shells under Edge Shock Loading of tangential, bending and normal types // In the collection: XI All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics. Collection of reports. Kazan. 2015. pp. 2008–2010, eLIBRARY ID: 24824460, EDN: UXGBTF
- Kirillova I.V., Kossovich L.Y. Asymptotic theory of wave processes in shells of revolution under shock surface and edge normal loads // Mechanics of Solids, 2022, no. 2, pp. 35–49. http://dx.doi.org/10.31857/S057232992202012X
- Kirillova I.V. Asymptotic theory of a hyperbolic boundary layer in shells of revolution under tangential-type edge shock loading // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, no. 2, pp. 222–230. https://doi.org/10.18500/1816-9791-2024-24-2-222-230
- Kirillova I.V. Asymptotic theory of nonstationary elastic waves in shells of revolution under bending-type edge shock loads // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, no. 1, pp. 80–90. https://doi.org/10.18500/1816-9791-2025-25-1-80-90
- Kirillova I.V. Hyperbolic boundary layer near the shear wavefront in shells of revolution // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, no. 3, pp. 394–401. https://doi.org/10.18500/1816-9791-2024-24-3-394-401
- Polyanin A.D., Manzhirov A.V. Handbook of Integral Equations. 2nd ed. Boca Raton: Chapman & Hall/CRC, Taylor & Francis Group, 2008. 1109 p. https://doi.org/10.1201/9781420010558
- Novozhilov V.V., Slepyan L.I. On Saint-Venant's principle in rod dynamics // PMM, 1965, vol. 29, no. 2, pp. 261–281.
- Slepyan L.I. Nonstationary Elastic Waves. Leningrad: Sudostroenie, 1972. 374 p. (in Russian)
- Dimitrienko Yu.I. Asymptotic theory of multilayer thin micropolar elastic plates // Mathematical Modeling and Computational Methods, 2023, no. 2(38), pp. 33–66. https://doi.org/10.18698/2309-3684-2023-2-3366
- Dimitrienko Yu.I. Asymptotic theory of multilayer thin elastic plates with interlayer slip // Mathematical Modeling and Computational Methods, 2022, no. 2(34), pp. 28–62. https://doi.org/10.18698/2309-3684-2022-2-2862
Supplementary files
