PROPAGATION PROPERTIES OF NONLINEAR OWN WAVES IN A VISCOELASTIC SHELL WITH LIQUID

Abstract

The present article deals with further developing of perturbation method for deformation non-linear waves in an elastic cylinder shell, filled with viscous incompressible liquid without inertia of its movement, surrounded by an elastic media and under constraction damping in longitudinal direction. Surrounding medium presence leads to integral-differential equation, to generalizing Korteweg-de Veries ones and possessing the same solution in the form of a solitary wave – a solution. It does not contain an arbitrary constant number unlike Korteweg-de Veries equation solution. The viscous incompressible liquid presence inside the shell behavior is described by means of dynamics and continuity rquation, is solved together with boundary conditions liquid adhesion to a shell wall. The numerical investication is carried out with the use of the modern approach, relying on the universial algorithm of communative algebra for integro-interpolation method. As a result of difference Grobner basis construction, the difference Crank-Nicolson type schemes are generalized. The schemes were obtained due to the use of basic integral difference correlations, approximating the initial equations system. Computational experiment showed that in the case of construction damping and liquid impact have opposite signs but coincide in value, their influence does not case and a solition propagates without changing its direction and its amplitude, which coincide analytical solution. If constructive damping exceeds liquid impact, the wave amplitude decreases, in the opposite case the wave amplitude grouse.