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
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.
Mogilevich L., Ivanov S.
The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside
2019, Vol. 15, no. 3, pp. 233-250
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 – 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 – de Vries – Burgers equation are adequate.