Abstract:

Currently, mathematical models are developed on the basis of the formulation and solution of problems of hydroelasticity. for studying of nonlinear wave processes in infinitely long geometrical nonlinear coaxial cylindrical shells between which there is a viscous liquid. These problems consist of systems of dynamics shell and viscous incompressible fluid equations, which are supplemented by boundary conditions at the boundaries of the contact "shell surface - liquid". These problems are described by shell dynamics and viscous incompressible liquid equations with corresponding. In this paper, the mathematical model for the study of wave processes in geometrically nonlinear Kirchhoff-Love shells, forming an annular channel filled with viscous incompressible fluid, surrounded by an elastic medium both outside and inside, is constructed and studied. The elastic medium model in which reactions in both normal and longitudinal direction are taken into account is considered.

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