Axisymmetric Forced Vibration of Hydro-Elastic System Consisting of Pre-Strained Highly Elastic Plate, Compressible Inviscid Fluid and Rigid Wall

Abstract

The present paper studies the axisymmetric forced vibrations of the hydro-elastic system consisting of the plate made of a highly elastic material with axisymmetric finite initial strains, barotropic inviscid compressible fluid, and rigid wall restricting the fluid flow. The motion of the plate is described using the equations and relations of the three-dimensional linearized theory of elastic waves in bodies with initial stresses. However, the flow of the fluid is described by the linearized Euler equations for the inviscid compressible fluids. Guz's presentations for the general solution of the mentioned linearized equations are used to solve these equations for the corresponding boundary and compatibility conditions. The corresponding equations concerning these transforms are solved analytically using the Hankel integral transform. The originals of the sought values are found numerically by employing the authors' calculation algorithm and PC programs. Numerical results on the frequency response of the interface pressure are presented and discussed. In particular, it is established that the initial radial stretching of the plate leads to the decrease in the interface pressure.