Modeling of Bending and Radial Hydroelastic Oscillations for a Sandwich Circular Plate Resting on an Inertial Elastic Foundation

Abstract

Abstract The paper deals with the development and analysis of a mathematical model for a circular sandwich plate resting an inertial elastic foundation and interacting with pulsating viscous liquid layer. The sandwich plate is the bottom wall of a channel containing a thin layer of viscous liquid. The pressure in the viscous liquid layer changes due to a predetermined pressure pulsation law at the channel contour and its squeeze between the upper channel wall and the vibrating circular sandwich plate. The coupled hydroelasticity problem consisting of the Navier-Stokes equations, the continuity equation, and the dynamics equations for the circular sandwich plate with corresponding boundary conditions was formulated and solved. We studied the viscous fluid motion inside the channel as a creeping one. The elastic foundation was considered in the framework of inertial Winkler foundation model. To write the sandwich plate dynamics equations, we used the kinematic hypothesis of the broken normal. The hydrodynamic parameters of the liquid layer, including its stresses acting on the sandwich plate, were found. The final mathematical model is the system of partial differential equations for studying bending and radial hydroelastic oscillations of the sandwich plate. Its investigation was carried out by the Fourier method. We studied plate dynamic behaviour in the main vibration mode. In particular, the frequency response of the circular sandwich plate were constructed and studied.