On the study of dynamic problems for layered-structured media with discontinuous boundary condition

Authors

  • Pavlova A.V. Kuban State University, Krasnodar, Российская Федерация
  • Rubtsov S.E. Kuban State University, Krasnodar, Российская Федерация
  • Telyatnikov I.S. Southern Scientific Centre of Russian Academy of Science, Rostov-on-Don, Российская Федерация

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-18-3-26-34

Abstract

The problems of vibration for bodies with a single defect or with a system of defects under the effect of loads in various formulations are considered in numerous works by a number of authors. The discovery of the localization of vibration processes in the vicinity of plane inhomogeneities was led by V.A. Babeshko to the creation of a theory that studies various combinations of defects and their influence on the dynamic properties of layered elastic media.
The theory of vibration resistance viruses has wide applications in various fields, among which one of the most important is seismology.
The paper presents an approach for solving the problems of oscillation for multilayer media with a single defect or with a system of defects such as rigid inclusions under the effect of harmonic loads based of the theory of vibration resistance viruses proposed by V.A. Babeshko. The obtained functional-matrix relations for the characteristics of the stress-strain state of a layer package containing a set of plane inclusions serve as the basis for the construction of an integral equations system for contact stresses in the area of a stamp effect and stress surges on the edges of inclusions. Factorization methods can be used for solving integral equations (IE) and systems for some special cases of the stamp bottom and inclusion forms.
In this work, we present the solution of the integral equation for the scalar problem with a single inclusion using the fictitious absorption method, and show the results of the calculations for the real part of the vertical component of the stress jump amplitude vector for a rigid inclusion in a three-layer package with a clamped bottom edge.
Along with such fields as seismology and geophysics, which study the stress-strain state of geological structures, the presented approach can find applications in materials science, defectoscopy, engineering practice, etc.

Keywords:

layered-structured medium, vibration resistance virus, rigid inclusions, integral equation, fictitious absorption method

Acknowledgement

Работа выполнена в рамках задания ГЗ ЮНЦ РАН, проект №~01201354241, отдельные результаты работы получены при поддержке РФФИ (проект 19-08-00145).

Author Infos

Alla V. Pavlova

д-р физ.-мат. наук, профессор кафедры математического моделирования Кубанского государственного университета

e-mail: pavlova@math.kubsu.ru

Sergei E. Rubtsov

канд. физ.-мат. наук, доцент кафедры математического моделирования Кубанского государственного университета

e-mail: rub_serg@mail.ru

Ilya S. Telyatnikov

канд. физ.-мат. наук, научный сотрудник лаборатории математики и механики Федерального исследовательского центра Южный научный центр Российской академии наук

e-mail: ilux_t@list.ru

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Issue

2021. Vol. 18. No. 2

Section

Mechanics

Pages

26-34

Submitted

2021-06-14

Published

2021-06-28

How to Cite

Pavlova A.V., Rubtsov S.E., Telyatnikov I.S. On the study of dynamic problems for layered-structured media with discontinuous boundary condition. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2021, vol. 18, no. 2, pp. 26-34. DOI: https://doi.org/10.31429/vestnik-18-3-26-34 (In Russian)

Copyright (c) 2021 Pavlova A.V., Rubtsov S.E., Telyatnikov I.S.

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