FORCED VIBRATION OF THE HYDRO-VISCOELASTIC AND -ELASTIC SYSTEMS CONSISTING OF THE VISCOELASTIC OR ELASTIC PLATE, COMPRESSIBLE VISCOUS FLUID AND RIGID WALL: A REVIEW

Abstract

The paper deals with the review of the investigations related to the study of the forced vibration of the hydro-viscoelastic and -elastic pre-stressed systems consisting of a prestressed layer, compressible viscous fluid and rigid wall. It is considered the investigations in which the motion of the plate is described within the scope of the three-dimensional linearized theory of wave propagation in viscoelastic bodies with initial stresses, however the motion of the fluid within the scope of the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluid. In the reviewed investigations it is assumed that on the plate the lineal-located time-harmonic moving load acts and the influence of the problem parameters such as fluid viscosity, fluid compressibility, fluid depth, plate thickness, rheological parameters of the plate material and etc., on the stresses and velocities on the interface plane between the plate and fluid is studied. Moreover, the problems related to the case where the plate moves with constant velocity and on the free plane on this plate the lineal-located time-harmonic force acts, is also considered. All the problems considered in the reviewed papers relate to the plane-strain state case in the plate and to the corresponding two-dimensional plane flow of the fluid. Throughout the paper some examples on the numerical results on the fluid flow velocity and pressure on the interface plane are presented and discussed. According to the reviewed results, it is proposed the further investigations fields in the study of the hydro-viscoelastic problems and, in particular, the necessity of the study the corresponding three-dimensional problems is indicated.