Mathematical modeling of incompressible viscous liquid layer interaction dynamics in an annular slit with its wall, surrounded by elastic medium

The dynamic hydroelasticity problem of annular channel outer wall, surrounded by elastic medium and interacting with highly viscous incompressible liquid, filling the channel, is considered. The inner wall, being an absolutely rigid cylinder of finite sizes, performs harmonic oscillations according to the assigned law. The second outer channel wall is formed by elastic cylinder shell, surrounded by elastic medium. The mathematical model of the channel under consideration is made. Cylinder deflections are modeled by elastic shifts of one-mass system, which parameters are found by using the method of the equivalent mass. The hydrodynamic parameters of viscous incompressible liquid layer in the channel, as well as outer channel wall shifts, are found. The obtained mathematical model allows investigating dynamic processes, conditioned by elastic elements interaction with viscous liquid in hydrodrives, power units and devices.