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Nelin. Dinam., 2019, Volume 15, Number 3, Pages 233–250 (Mi nd656)  

Nonlinear physics and mechanics

The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside

L. I. Mogilevicha, S. V. Ivanovb

a Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya 77, Saratov, 410054 Russia
b Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia

Abstract: This article is devoted to studying longitudinal deformation waves in physically nonlinear elastic shells with a viscous incompressible fluid inside them. The impact of construction damping on deformation waves in longitudinal and normal directions in a shell, and in the presence of surrounding medium are considered.
The presence of a viscous incompressible fluid inside the shell and the impact of fluid movement inertia on the wave velocity and amplitude are taken into consideration. In the case of a shell filled with a viscous incompressible fluid, it is impossible to study deformation wave models by qualitative analysis methods. This makes it necessary to apply numerical methods. The numerical study of the constructed model is carried out by means of a difference scheme analogous to the Crank Ц Nickolson scheme for the heat conduction equation. The amplitude and velocity do not change in the absence of surrounding medium impact, construction damping in longitudinal and normal directions, as well as in the absence of fluid impact. The movement occurs in the negative direction, which means that the movement velocity is subsonic. The numerical experiment results coincide with the exact solution, therefore, the difference scheme and the modified Korteweg Ц de Vries Ц Burgers equation are adequate.

Keywords: nonlinear waves, elastic cylinder shell, viscous incompressible fluid, Crank Ц Nickolson difference scheme

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00014a
The work was supported by the RFBR grant No. 19-01-00014a.


DOI: https://doi.org/10.20537/nd190303

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MSC: 74J30
Received: 10.04.2019
Accepted:15.07.2019

Citation: L. I. Mogilevich, S. V. Ivanov, “The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside”, Nelin. Dinam., 15:3 (2019), 233–250

Citation in format AMSBIB
\Bibitem{MogIva19}
\by L. I. Mogilevich, S. V. Ivanov
\paper The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 3
\pages 233--250
\mathnet{http://mi.mathnet.ru/nd656}
\crossref{https://doi.org/10.20537/nd190303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4021366}


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