WAVE PROPAGATION IN COAXIAL NON-LINEAR ELASTIC CYLINDRICAL SHELLS, CONTAINING VISCOUS INCOMPRESSIBLE LIQUID WITH INERTIA OF ITS MOVEMENT
1. Yuri Gagarin State Technical University of Saratov
2. Volga Management Institute named after P.А. Stolypin - a branch of Federal State-Funded Educational Institution of Higher Education Russian Presidential Academy of National Economy and Public Administration
3. Saratov State University
4. Industrial Automatics Design Bureau JSC
There exist models of wave motions in infinitely long geometrically non-linear shells, containing viscous incompressible liquid without inertia of its movement, in the form of generalized KdV equations. Also, mathematical models of the wave process in cylindrical elastic shells. These models differ from the known ones by the consideration of incompressible liquid presence between the shells, based on the related hydroelasticity problems. These problems are described by shells dynamics and viscous incompressible liquid equations without inertia of its movement in the form of generalized KdV equations system. The paper presents the investigation of wave occurrences of two geometrically non-linear elastic coaxial cylindrical shells, containing viscous incompressible liquid with inertia of its movement between them, as well as inside. The difference schemes of Crank-Nicholson type are obtained for the considered equations system. On the basis of computation algorithm the complex of programs, permitting to construct graphs and obtain numerical solutions, was made.
Keywords: nonlinear waves, viscous incompressible liquid, elastic cylinder shell