Abstract:

The article is devoted to studying longitudinal deformation waves in physically non-linear elastic shells with viscous incompressible liquid inside them. Viscous incompressible liquid presence inside the shell and liquid movement inertia impact on the wave velocity and amplitude are taken into consideration. It is impossible to study deformation waves models, in case of the shell filling with viscous incompressible liquid, by means of qualitative analysis methods. Then the necessity of numerical methods application arises. The numerical study of the constructed model is carried out by means of difference scheme, analogous to Crank-Nickolson one for the Heat conducting equation. The amplitude and velocity do not change under absence of liquid impact movement. The movement occurs in the negative direction, which means that movement velocity is subsonic. The numerical experiment result consider with exact solution, therefore, difference scheme and modified Korteweg–de Vries equation are adequate. The presence of liquid movement inertia impact leads to deformation wave velocity reducing, while liquid viscous tension on the shell leads to wave amplitude falling.

Keywords: Crank-Nickolson difference scheme, viscous incompressible liquid, elastic cylinder shell, non-linear waves