Abstract:

The problems of viscous incompressible liquid movement in an elastic cylinder shell as of circular, as well as of annular cross-sections under the impact of some factors are considered. All these problems contain the systems “liquid – elastic body” movement sources. To reveal dynamic characteristic of these systems, it is necessary to solve the connected problems of an elastic shell and viscous incompressible liquid dynamics. The factor, making the problem simpler, is a small size of a shell radius in comparison with its length, as in lubrication theory. The problems under consideration contain this supposition about a small size of the shell sagging in comparison with a shell radius, or liquid layer thickness, but not with a shell thickness. Under these conditions hydrodynamics equations become linear. The elastic elements dynamics equations remain non-liner, if they were such initially. If it is not possible to find the exact solution, the iteration method for solving the lubrication theory hydrodynamics equations applied.

Keywords: viscous liquid, elastic shell, oscillations, waves