The influence of the rheological parameters of a hydro-viscoelastic system consisting of a viscoelastic plate, viscous fluid and rigid wall on the frequency response of this system

Abstract

In this paper the forced vibration of a hydro-viscoelastic system consisting of a viscoelastic plate, compressible viscous fluid and rigid wall is considered. The focus is on the investigation of the influence of the rheological parameters of the plate material and the viscosity of the fluid on the frequency response of this system. The constitutive relations for the plate material are given through the fractional-exponential operators, and the exact equations of the visco-elastodynamics in the plane-strain state are employed for describing the plate motion. The fluid motion is described through the linearized Navier-Stokes equations and it is assumed that the velocity and force vectors are continuous across the interface plane between the fluid and the plate. Numerical results on the frequency response of the normal stress acting on the interface plane and of the normal velocity of the points of this plane are presented for various values of the rheological parameters of the plate material. These results are also distinguished with respect to inviscid and viscous fluid cases. As a result of the analyses of these results, corresponding conclusions are made on the influence of the rheological parameters of the plate material on the aforementioned frequency responses.