Abstract:

The problem of damping and basis dynamics of viscous incompressible liquid is considered under interaction with an elastic stator. It may take the form of an elastic circular plate. Besides the stator considered may represent a circular three-layered elastic plate or a geometrically irregular one (with rigidity rib). The vibrator may be elastic or absolutely solid. 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 plate and viscous incompressible liquid dynamics. The factor, making the problem simpler, is a small thickness of liquid layer in comparison with a linear size of the plate, as in lubrication theory. The problems under consideration contain this supposition about a small size of stator’s movements amplitude in comparison with liquid layer thickness, but not with a plates 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 plates, oscillations, waves.