Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Kirillova I. V. Asymptotic theory of the transient waves in shells of revolution at shock edge loading of the bending type. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 1, pp. 80-90. DOI: 10.18500/1816-9791-2025-25-1-80-90, EDN: SUWSYV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.02.2025
Full text:
download
(downloads: 73)
Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2025-25-1-80-90
EDN: 
SUWSYV

Asymptotic theory of the transient waves in shells of revolution at shock edge loading of the bending type

Autors: 
Kirillova Irina V., Saratov State University
Abstract: 

The present work is devoted to completing the construction of the nonstationary stress-stain state asymptotic theory of shells of revolution at shock edge bending loading. There components with different values of the variability and dynamicity indices are used. This asymptotic model applies such components as the bending component of the Kirchoff – Love shell theory, the antisymmetric high-frequency short-wave component and the antisymmetric hyperbolic boundary layer in the vicinity of the dilatation wave front. The existence of the overlap regions is indicative of the exact statement of the boundary value problems for all the components and of the validity of the introduced separation scheme.

Key words: 
asymptotic theory
bending component
high-frequency short-wave component
hyperbolic boundary layer
dilatation wave front
overlap region
shell of revolution
References: 
  1. Kossovich L. Yu. Nestatsionarnye zadachi teorii uprugikh tonkikh obolochek [Non-stationary problems of the theory of elastic thin shells]. Saratov, Saratov State University Publ., 1986. 176 p. (in Russian). EDN: VIOSWL
  2. Kaplunov J. D., Nolde E. V., Kossovich L. Y. Dynamics of thin walled elastic bodies. San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, Academic Press, 1998. 226 p.. https://doi.org/10.1016/C2009-0-20923-8, EDN: WNSAFB
  3. Nigul U. K. 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, iss. 6, pp. 607–627. https://doi.org/10.1016/0020-7683(69)90031-6
  4. Goldenveizer A. L. Theory of elastic thin shells. Oxford, Pergamon Press, 1961. 658 p. (Russ. ed.: Moscow, Nauka, 1976. 512 p.).
  5. Novozhilov V. V., Slepian L. I. On Saint-Venant’s principle in the dynamics of beams. Journal of Applied Mathematics and Mechanics, 1965, vol. 29, iss. 2, pp. 293–315. https://doi.org/10.1016/0021-8928(65)90032-8
  6. Slepian L. I. Nestatsionarnye uprugie volny [Unsteady elastic waves]. Leningrad, Sudostroenie, 1972. 374 p. (in Russian).
  7. Kossovich L. Yu., Kirillova I. V. Dynamics of shells under shock loading: an asymptotic approach. Civil-Comp Proceedings, 2008, vol. 88, pp. 1–20. EDN: QPMORG
  8. Kossovich L. Yu., Kirillova I. V. Asymptotic theory of non-stationary processes in thin shells. Proceedings of the Second International Conference Topical Problems of Continuum Mechanics. Dilijan, Armenia, 2010, pp. 321–325 (in Russian).
  9. Kaplunov Yu. D., Kirillova I. V., Kossovich L. Yu. Asymptotic integration of the dynamic equations of the theory of elasticity for the case of thin shells. Journal of Applied Mathematics and Mechanics, vol. 57, iss. 1, pp. 83–91 (in Russian). EDN: UJSTAN
  10. Kirillova I. V. Asymptotic theory of the hyperbolic boundary layer in shells of revolution at shock edge loading of the tangential type. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 2, pp. 222–230 (in Russian). https://doi.org/10.18500/1816-9791-2024-24-2-222-230, EDN: SFYWBV
  11. Kirillova I. V., Kossovich L. Yu. Asymptotic theory of wave processes in shells of revolution under surface impact and normal end actions. Mechanics of Solids, 2022, vol. 57, iss. 2, pp. 232–243. https://doi.org/10.3103/S0025654422020078, EDN: WCTBUQ
  12. Nigul U. K. On the methods and the results of analysis of transient wave processes of bending of an elastic plate. Eesti NSV Teaduste Akadeemia Toimetised. Füüsika-, Matemaatika- ja Tehnikateaduste Seeria, 1965, vol. 14, iss. 3, pp. 345–384 (in Russian). https://doi.org/10.3176/phys.math.tech.1965.3.04
  13. Nigul U. K. On the applicability of approximate theories in transient processes of deformations of circular cylindrical shells. Trudy 6-y Vsesoyuznoy konferentsii po teorii obolochek i plastin [Proceedings of the 6th All-Union Conference on the Theory of Shells and Plates]. Moscow, Nauka, 1966, pp. 593–599 (in Russian).
  14. Nigul U. K. Comparison of the results of the analysis of transient wave processes in shells and plates according to the theory of elasticity and approximate theories. Applied Mathematics and Mechanics, 1969, vol. 33, iss. 2, pp. 308–322 (in Russian).
  15. Kirillova I. V. Asymptotic derivation of two types of approximation of dynamic equations of the theory of elasticity for thin shells. Diss. Cand. Sci. (Phys.-Math.). Saratov, 1998. 122 p. (in Russian).
Received: 
21.10.2024
Accepted: 
19.11.2024
Published: 
28.02.2025
  • 151 reads