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Russian Journal of Nonlinear Dynamics, 2020, Volume 16, Number 2, Pages 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
References:
Abstract: 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.
Keywords: nonlinear waves, elastic cylindrical shells, viscous incompressible fluid, Crank – Nicolson difference scheme.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00014a
This work was supported by the RFBR grant No. 19-01-00014a.
Received: 30.11.2019
Accepted: 30.01.2020
Bibliographic databases:
Document Type: Article
MSC: 74J30
Language: English
Citation: 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
Citation in format AMSBIB
\Bibitem{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}
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