- PII
- 10.31857/S0032823523020030-1
- DOI
- 10.31857/S0032823523020030
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 87 / Issue number 2
- Pages
- 303-313
- 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.
- Keywords
- контактная задача блочный элемент деформируемый штамп интегральное уравнение Винера–Хопфа
- Date of publication
- 01.02.2023
- Year of publication
- 2023
- Number of purchasers
- 0
- Views
- 32
References
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