Features of dynamics of three-layer hollow cylinder

Authors

  • Belyankova T.I. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация
  • Kalinchuk V.V. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация
  • Lyzhov V.A. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация

UDC

539.3

Abstract

An effective method is proposed for constructing the Green matrix-function of an infinite circular cylinder with a layered inhomogeneous coating. As the cover, the multilayer cylinder wall is considered, which consist of the package of embedded both homogeneous and functionally graded cylinders, rigidly coupled together. The method is based on the use of the operational calculus apparatus in combination with the analytical (for homogeneous) or numerical (for inhomogeneous coating components) construction of solution, followed by the matrix approach while satisfying the boundary conditions. The proposed approach for modeling a layered inhomogeneous coating allows to take adequately into account both the differences in the change of physical and mechanical properties of the coating components, and the possible differences in the conditions at their interface. The matrix formulas convenient for programming are constructed, which allow not only to investigate the dispersion properties with high precision, but also to solve the mixed dynamic problems on vibrations of both hollow and liquid-filled inhomogeneous cylinder. On the example of the problem for torsional oscillations of the bandage on the surface of two and three layer hollow cylinder, a detailed analysis is carried out for the influence of the physical and mechanical properties relation, nature, localization region and intensity of changes in the properties of the hollow cylinder wall on its dynamic stiffness. The regularities are established that allow to optimize the pipeline technical, operational and strength qualities by changing the structure and properties of the pipeline wall.

Keywords:

layered-inhomogeneous medium, thick-walled hollow cylinder, multilayer coating, functionally graded material, Green's function, torsional oscillations, integral equation, dynamic stiffness

Acknowledgement

Работа выполнена при финансовой поддержке РФФИ (проекты 13-08-96528-р-юг, 15-08-0674, 14-08-01213).

Author Infos

Tatyana I. Belyankova

канд. физ.-мат. наук, доц., ведущий научный сотрудник отдела механики авиационных и нанотехнологий Южного научного центра РАН, ведущий научный сотрудник Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

e-mail: tbelen415@mail.ru

Valeriy V. Kalinchuk

д-р физ.-мат. наук, заместитель Председателя Южного научного центра РАН, заведующий лабораторией Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

e-mail: kalin@ssc-ras.ru

Vyacheslav A. Lyzhov

канд. физ.-мат. наук, научый сотрудник отдела механики авиационных и нанотехнологий Южного научного центра РАН, младший научный сотрудник Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

e-mail: maggod-rnd@yandex.ru

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Issue

2015. No. 4

Pages

19-32

Submitted

2015-12-19

Published

2015-12-28

How to Cite

Belyankova T.I., Kalinchuk V.V., Lyzhov V.A. Features of dynamics of three-layer hollow cylinder. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 4, pp. 19-32. (In Russian)

Copyright (c) 2015 Belyankova T.I., Kalinchuk V.V., Lyzhov V.A.

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