Dispersion of the axisymmetric waves propagating in the hydro-elastic system consisting of the pre-strained highly elastic plate, compressible inviscid fluid, and rigid wall

The paper deals with the study of the influence of the homogeneous finite initial strains in a highly elastic plate which is in contact with a compressible inviscid fluid on the dispersion of the axisymmetric waves propagating in the “plate + fluid” and “plate + fluid + rigid wall” systems. It is assumed that the homogeneous finite initial strains in the plate are caused by the radial forces acting at infinity, and the motion of the plate is described by the three-dimensional linearized equations and relations of elastic waves in bodies with initial stresses. The fluid flow is formulated by the linearized Navier–Stokes equations for compressible barotropic inviscid fluids. Elasticity relations for the plate material are presented through the harmonic potential. It is established that as a result of the difference between the initial strain states appearing in the axisymmetric and plane-strain states in the plate, the dispersion equation obtained for the studied dynamic problem does not coincide with the dispersion equation obtained for the corresponding plane-strain state. The dispersion curves are constructed for various values of the initial strains in the case where the material of the plate is soft-rubber, and the fluid is taken as water. From analysis of these curves, in particular, it is established that the initial strains not only quantitatively, but also qualitatively influence the dispersion of the axisymmetric waves propagating in the hydro-elastic system under consideration.