Abstract:

The paper investigates longitudinal waves in coaxial elastic shells with soft cubic nonlinearity, containing a viscous incompressible fluid, both between them and in the inner shell. The influence of the viscosity and inertia of fluid motion, structural damping of the shell material in the normal one on the wave amplitude and speed are taken into account. It is impossible to study the models of deformation waves by the methods of qualitative analysis in the case of filling the inner shell with a viscous incompressible fluid. This leads to the need for numerical methods. In the absence of the influence of the liquid inside the shell, the velocity and amplitude of the waves presented in the shells do not change. The movement takes place in the negative direction of the abscissa axis. This means that the found nonlinear addition to the wave velocities in the linear approximation (the speed of sound) reduces the wave velocities and they become subsonic. The presence of the influence of the inertia of motion of the liquid in the inner shell leads to a decrease in the velocity of the deformation waves. The viscous stress of the liquid in the inner shell leads to a decrease in the waves´ amplitudes. Structural damping in the normal direction enlarges wave amplitude and reduces the wave velocity. ____________________________________________________________________________________________________________________________________________________ https://doi.org/10.24411/2541-9269-2020-00004

Keywords: viscous incompressible liquid, elastic cylinder shell, non-linear waves