Russian Journal of Nonlinear Dynamics
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Russian Journal of Nonlinear Dynamics, 2020, том 16, номер 2, страницы 275–290
DOI: https://doi.org/10.20537/nd200204
(Mi nd710)
 

Nonlinear physics and mechanics

Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion

L. I. Mogilevicha, S. V. Ivanovb, Yu. A. Blinkovb

a Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya 77, Saratov, 410054 Russia
b Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
Список литературы:
Аннотация: This article investigates longitudinal deformation waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid between them. The rigid nonlinearity of the shells is considered. The presence of a viscous incompressible fluid between the shells, as well as the influence of the inertia of the fluid motion on the amplitude and velocity of the wave, are taken into account.
A numerical study of the model constructed in the course of this work is carried out by using a difference scheme for the equation similar to the Crank – Nicolson scheme for the heat equation.
In the case of identical initial conditions in both shells, the deformation waves in them do not change either the amplitude or the velocity. In the case of setting different initial conditions in the coaxial shells, the amplitude of the solitary wave in the first shell decreases from the value specified at the initial instant of time, and in the second, the amplitude grows from zero until they equalize, that is, energy is transferred.
The movement occurs in a negative direction. This means that the velocity of deformation wave is subsonic.
Ключевые слова: nonlinear waves, elastic cylindrical shells, viscous incompressible fluid, Crank – Nicolson difference scheme.
Финансовая поддержка Номер гранта
Российский фонд фундаментальных исследований 19-01-00014a
This work was supported by the RFBR grant No. 19-01-00014a.
Поступила в редакцию: 30.11.2019
Принята в печать: 30.01.2020
Реферативные базы данных:
Тип публикации: Статья
MSC: 74J30
Язык публикации: английский
Образец цитирования: L. I. Mogilevich, S. V. Ivanov, Yu. A. Blinkov, “Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion”, Rus. J. Nonlin. Dyn., 16:2 (2020), 275–290
Цитирование в формате AMSBIB
\RBibitem{MogIvaBli20}
\by L. I. Mogilevich, S. V. Ivanov, Yu. A. Blinkov
\paper Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 2
\pages 275--290
\mathnet{http://mi.mathnet.ru/nd710}
\crossref{https://doi.org/10.20537/nd200204}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093897173}
Образцы ссылок на эту страницу:
  • https://www.mathnet.ru/rus/nd710
  • https://www.mathnet.ru/rus/nd/v16/i2/p275
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