Abstract:

The investigation of deformation waves behavior in elastic shells is one of the important trends in the contemporary wave dynamics. There exist mathematical models of wave motions in infinitely long geometncally non-linear shells, containing viscous incompressible liquid based on the related hydroelasticity problems, which are derived by the she´! dynamics and viscous incompressible liquid equations in the form of ceneralized Korteweg - de Vnes (KdV) equations. In addition, mathematical models or the wave process in infinitely long geometncally non-linear coaxial cylindrical elastic shells are obtained by the perturbation method. These models differ from the known ones by the consideration of incompressible liquid between the shells, based on the lelated hydroelasticity problems. These problems are described by shell dynamics and viscous incompressible liquid equations with corresponding edge conditions in the form of generalized KdV equation svstem. The paper presents the investigation of wave occurrences in two geometrically non-linear elastic coaxial cylindrical shells of Kirchhoff-Love type, containing viscous incompressible liquid between them, and surrounded by an elastic Medium, acting in both normal and longitudinal directions.

Keywords: nonlinear waves, viscous incompressible liquid, elastic cylindrical shells