Axisymmetric forced vibration of the hydro-elastic system consisting of a pre-strained highly elastic plate and compressible viscous fluid

Abstract

The paper studies the axisymmetric harmonic forced vibration of the hydro-elastic system composed of an initially strained plate made of highly elastic material, a compressible viscous fluid layer, and a rigid wall restricting the fluid flow. It is assumed that the plate is in contact with the fluid layer after the appearance of the finite axisymmetric homogeneous initial strains within which are caused by the stretching of the plate by uniformly distributed radial forces acting at infinity. Also, it is assumed that after this contact, the point located time-harmonic force begins to act on the free-face plane of the plate. Within this framework, the steady-state forced vibration of the hydro-elastic system under consideration is studied by employing the eq. and relations of the so-called three-dimensional linearized theory of elastic waves in bodies with finite initial strains to describe the motion of the plate and by employing the linearized Navier-Stokes eq. to describe the flow of the fluid. The corresponding mathematical problem is solved by employing the Hankel integral transform method, and the originals of the sought values are found numerically by employing the algorithms and PC programs composed by the authors. Numerical results are presented and discussed on the frequency response of the normal stress acting on the interface plane between the plate and fluid layer. According to these discussions, corresponding conclusions on the influence of the problem parameters on the frequency response of the interface stress are made. In particular, it is established that in the axisymmetric forced vibration case, the resonance-type phenomenon appears due to the fluid viscosity.