Simulating Wave Processes in Two Shells Separated by Liquid and Surrounded by an Elastic Medium
Authors: Blinkov Yu.A., Evdokimova E.V., Mogilevich L.I., Rebrina A.Yu. | Published: 05.12.2018 |
Published in issue: #6(81)/2018 | |
DOI: 10.18698/1812-3368-2018-6-4-17 | |
Category: Mathematics and Mechanics | Chapter: Mathematical Physics | |
Keywords: nonlinear waves, viscous incompressible fluid, elastic cylindrical shells, Grobner basis |
There exist mathematical models of wave motion in infinitely long geometrically nonlinear shells containing viscous incompressible fluid. These are based on related hydroelasticity problems described by equations of shell and viscous incompressible fluid dynamics in the form of generalised Korteweg --- de Vries equations. Having identified the small parameter of the problem, we used the perturbation method to obtain mathematical models of the wave process in elastic infinitely long geometrically nonlinear coaxial cylindrical shells. These models take the form of a system of generalised Korteweg --- de Vries equations. They are different from the ones known previously since they account for the presence of viscous incompressible fluid between shells. The paper investigates the models of wave phenomena occurring in two elastic geometrically nonlinear coaxial cylindrical Kirchhoff --- Love shells separated by a layer of viscous incompressible fluid and surrounded by an elastic medium acting both normally and longitudinally. We constructed a Grobner basis to derive difference schemes of the Crank --- Nicolson type for the systems of equations under consideration, accounting for the effect of the fluid. We generated these difference schemes using fundamental integral relations in finite difference form that approximate the initial system of equations
The study was supported by RFBR (project no. 16-01-00175-a)
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