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On the Contact Problem with Deformable Stamp in the Quarter Plain
- Authors: Babeshko V.A.1,2, Evdokimova O.V.1, Babeshko O.M.2, Zaretskaya M.V.2, Evdokimov V.S.2
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Affiliations:
- Southern Scientific Center of the Russian Academy of Sciences
- Kuban State University
- Issue: Vol 87, No 2 (2023)
- Pages: 303-313
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138859
- DOI: https://doi.org/10.31857/S0032823523020030
- EDN: https://elibrary.ru/TYZHJI
- ID: 138859
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Abstract
In this paper, for the first time, a two-dimensional dynamic contact problem on the action of a deformable stamp on a quarter of the plane of a multilayer medium is strictly mathematically investigated. In contrast to the case of an absolutely solid stamp, a deformable stamp introduces additional features, consisting in the possibility of the occurrence of discrete resonances predicted by academician I.I. Vorovich. The paper shows that the use of a method based on the use of block elements makes it possible to obtain an equation describing resonant frequencies. To study contact problems with a deformable stamp made of materials of complex rheology, including smart materials, it is proposed in the paper to first conduct a study for the case of a deformable stamp made of a material of simple rheology described by Helmholtz equations. Solutions of boundary value problems for stamps of complex rheology, after that, are represented by a combination of solutions of boundary value problems for stamps of simple rheology.
About the authors
V. A. Babeshko
Southern Scientific Center of the Russian Academy of Sciences; Kuban State University
Author for correspondence.
Email: babeshko41@mail.ru
Russia, Rostov-on-Don; Russia, Krasnodar
O. V. Evdokimova
Southern Scientific Center of the Russian Academy of Sciences
Author for correspondence.
Email: evdokimova.olga@mail.ru
Russia, Rostov-on-Don
O. M. Babeshko
Kuban State University
Author for correspondence.
Email: babeshko49@mail.ru
Russia, Krasnodar
M. V. Zaretskaya
Kuban State University
Author for correspondence.
Email: zarmv@mail.ru
Russia, Krasnodar
V. S. Evdokimov
Kuban State University
Author for correspondence.
Email: evdok_vova@mail.ru
Russia, Krasnodar
References
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