Lev Mogilevich
Publications:
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Mogilevich L., Ivanov S., Blinkov Y.
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
2020, Vol. 16, no. 2, pp. 275-290
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.
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