On the Contact Problem with Deformable Stamp in the Quarter Plain

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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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  2. Vorovich I.I. Resonant properties of an elastic inhomogeneous band // Dokl. akad. nauk SSSR, 1979, vol. 245, no. 5, pp. 1076–1079. (in Russian)
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  16. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Exact Solution to the Contact Problem in a Quarter-Plane of a Multilayer Medium by the Universal Simulation Method // Mech. Solids, 2022, vol. 57, no. 8, pp. 2058–2065. doi: 10.3103/S0025654422080039

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Copyright (c) 2023 В.А. Бабешко, О.В. Евдокимова, О.М. Бабешко, М.В. Зарецкая, В.С. Евдокимов