The forced vibration of the system consisting of an elastic plate, compressible viscous fluid and rigid wall

Abstract

The forced vibration of the system consisting of a pre-stressed elastic plate, barotropic compressible Newtonian viscous fluid and rigid wall is considered. The space between the plate and rigid wall is filled by the fluid. It is assumed that the forced vibration is caused by the lineally-located time-harmonic force acting on the free face plane of the plate. The motion of the plate is written by utilizing the exact equations of elastodynamics, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Moreover, it is assumed that the velocities and stresses of the constituents are continuous on the contact plane between the plate and fluid, and that the impermeability conditions on the rigid wall are satisfied. The dimensionless parameters which characterize the compressibility and viscosity of the fluid as well as the elasticity constants of the plate are introduced. Plane strain state in the plate and two-dimensional plane flow of the fluid are considered. Numerical results on the interface normal stress and velocities are presented. The influence of the problem parameters is also discussed, including the fluid viscosity and compressibility, thickness of the plate and fluid depth as well as the excitation frequency. In this discussion the focus is on the influence of the fluid depth on the studied quantities. This is the parameter through which the main difference arises between the present and previous works by the authors.

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

“…The numerical results, which are discussed below, relate to the normal stress T22 acting on the interface plane between the fluid and plate and to the velocity v 2 of the fluid on the interface plane in the direction of the Ox2-axis. The investigations carried out in the works by Akbarov and Ismailov (2014a, 2015a, 2015b) show that the values of T22 and v 2 obtained in the cases where the fluid is modeled as viscous are comparable with the corresponding ones obtained in the case where the fluid is modeled as inviscid. These investigations also show that the values of v1 (i.e.…”

“…Up to now, investigations of the dynamics of hydro-viscoelastic systems have been almost completely absent. However, investigations of problems related to the corresponding hydro-elastic systems have developed quite well and a detailed review of them was made in the papers by Akbarov and Ismailov (2015a, 2015b). Nevertheless, here we also briefly review them and begin with the paper by Lamb (1921) in which a circular elastic “baffled” plate in contact with still water was studied by employing the so-called “nondimensional added virtual mass incremental” (NAVMI) method.…”

“…Employment of the aforementioned exact three-dimensional field equations on the study of the forced vibration of the hydro-elastic system consisting of a pre-strained highly elastic plate and compressible viscous fluid filling a half-plane was first made in the paper by Akbarov and Ismailov (2014a). The forced vibration of the system consisting of an elastic plate, compressible viscous fluid with finite depth and rigid wall was studied in the paper by Akbarov and Ismailov (2015b). Moreover, in the paper by Akbarov and Ismailov (2015a), the dynamics of the moving load acting on the aforementioned system were studied.…”

“…Therefore, in the present paper for determination of the aforementioned influence, the vibration of a hydro-viscoelastic system consisting of a viscoelastic plate, compressible viscous fluid and rigid wall is studied. In other words, in the present paper the problem considered in the paper by Akbarov and Ismailov (2015b) is developed for the case where the plate material is viscoelastic. The motion of the plate is described by employing the exact equations of visco-elastodynamics in the plane-strain state and the fluid flow is written by the use of the linearized Navier–Stokes equations.…”

Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

“…Akbarov, M.I. Ismailov where the motion of the plate is described by three‐dimensional linearized equations of wave propagation in elastic bodies with initial stresses, and the liquid flow is described with linearized Navier‐Stokes equations. The problems of non‐linear oscillations of plates moving in an ideal incompressible liquid were studied in works [].…”