For citation:
Kirillova I. V. Hyperbolic boundary layer in the vicinity of the shear wave front in shells of revolution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 3, pp. 394-401. DOI: 10.18500/1816-9791-2024-24-3-394-401, EDN: JMEGQP
Hyperbolic boundary layer in the vicinity of the shear wave front in shells of revolution
Hyperbolic boundary layer equations in thin shells of revolution are constructed in small vicinities of the shear wave fronts (taking into account its geometry) at edge shock loading of the normal type. Special coordinate system is used for defining the small boundary layer region. In this system, the coordinate lines defined by the normal to the middle surface are replaced by lines forming the surface of the shear wave front. The asymptotic model of the geometry of such a wave front suggests that these lines are formed by rotated normal to the middle surface. Asymptotically main components of considered stress strain state are defined: the normal displacement and the shear stress. The governing equation of this boundary layer is the hyperbolic equation of the second order with the variable coefficients for the normal displacement.
- 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
- 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
- Kirillova I. V., Kossovich L. Yu. Dynamic boundary layer at nonstationary elastic wave propagation in thin shells of revolution. AiM’96: Proceedings of the Second International Conference “Asymptotics in mechanics”. Saint Petersburg State Marine Technical University, Saint Petersburg, Russia, October 13–16, 1996. St. Petersburg, 1997, pp. 121–128.
- 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).
- Kirillova I. V., Kossovich L. Y. 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
- 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
- Slepian L. I. Nestatsionarnye uprugie volny [Unsteady Elastic Waves]. Leningrad, Sudostroenie, 1972. 374 p. (in Russian).
- Cole J. D. Perturbation Methods in Applied Mathematics. Blaisdell Publishing Company, Waltham, Massachusetts, 1968. 260 p. (Russ. ed.: Moscow, Mir, 1972. 274 p.).
- Goldenveizer A. L. Theory of Elastic Thin Shells. Oxford, Pergamon Press, 1961. 658 p. (Russ. ed.: Moscow, Nauka, 1976. 512 p.).
- 179 reads