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.