Axisymmetric forced vibration of the elastic plate in contact with a compressible viscous fluid layer

Abstract

The paper studies the axisymmetric frequency response of the hydro-elastic system consisting of an elastic plate, barotropic compressible viscous fluid, and rigid wall under the action on the plate a point-located time-harmonic force. The motion of the plate is described by utilizing the exact equations of linear elastodynamics. The fluid flow is defined by the linearized Navier-Stokes equations for compressible viscous fluids. For the solution to the problem, the Hankel integral transform is employed and the transforms for the sought quantities are found analytically from the solution of the corresponding field equations. The inverse of these transforms is found numerically by employing the corresponding algorithms and PC programs. Numerical results are presented for the frequency response of the normal stress (pressure) on the interface plane between the fluid and plate. In obtaining these results, it is assumed that the plate material is steel or Lucite, however, Glycerin or water is taken as the fluid. Based on these results, the influence of the problem parameters, such as fluid viscosity, fluid depths, and vibration phase on these frequency responses under various plate thicknesses is studied.