Hydroelastic response of a circular sandwich plate interacting with a liquid layer

Abstract

We considered the formulation and solution of the forced oscillations hydroelasticity problem for a three-layered circular plate contacting with a viscous incompressible fluid layer, the pressure in which varies according to the harmonic law. The plate is the bottom wall of a narrow channel completely filled with a viscous fluid. The axisymmetric coupled hydroelasticity problem consisting of the plate dynamics equation, the viscous fluid layer dynamics equation, and their corresponding boundary conditions was investigated. We obtained the plate dynamics equations taking into account inertia forces in the radial and normal directions in the framework of zigzag kinematic theory. In these equations, the load was expressed by the stresses of the viscous fluid contacting with the three-layered circular plate. The fluid dynamics equations were represented by the Navier-Stokes equations and continuity equation written for the case of creeping fluid flow in a channel. We obtained the forced radial and bending hydroelastic oscillations equations of the circular three-layered plate using the perturbation method. The solution of these equations was represented by a series of eigenfunctions of the corresponding Sturm-Liouville problem. We have also presented the numerical study results of the radial and bending vibrations amplitude dependence on the frequency for the main steady oscillations mode of the plate.