Abstract
Longitudinal and bending oscillations of a three-layer plate interacting with vibrating stamp through a thin layer of a viscous incompressible fluid are investigated. We study the plane problem. The plate is considered as a three-layer package consisting of two bearing layers with an incompressible filler between them. The broken normal hypothesis is used to cinematically describe a three-layer package. A mathematical model including Navier-Stokes equations, continuity equation and three-layer plate dynamics equations with the corresponding boundary conditions is developed. No-slip conditions, pressure conditions at the channel edges and simply supported plate edges conditions are selected as boundary ones. The hydrodynamic parameters distribution laws of the liquid layer and the elastic displacements of the three-layer plate are found by mines of the perturbation method.
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