Geodesic
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
Russian journal of nonlinear dynamics, Tome 16 (2020) no. 2, pp. 275-290

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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, Crank – Nicolson difference scheme.
Mots-clés : viscous incompressible fluid 
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     author = {L. I. Mogilevich and S. V. Ivanov and Yu. A. Blinkov},
     title = {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}},
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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. Russian journal of nonlinear dynamics, Tome 16 (2020) no. 2, pp. 275-290. http://geodesic.mathdoc.fr/item/ND_2020_16_2_a3/