Mathematical modeling of circular sandwich plate interaction with viscous liquid layer for predicting its hydroelastic response

Abstract

The paper proposes a mathematical model for predicting the hydroelastic response of a mechanical system consisting of a circular sandwich plate forming the bottom wall of a narrow channel filled with a pulsating viscous liquid. The pressure pulsation in the liquid layer is caused by upper vibrating channel wall represented by a rigid disk. We needed to formulate and solve the hydroelasticity problem for developing the mathematical model. The hydroelasticity problem consisted of the Navier-Stokes equations, the continuity equation, the circular sandwich plate dynamic equations, and the corresponding boundary conditions. The viscous liquid layer movement was assumed as a creeping one. We studied the stationary axisymmetric hydroelastic oscillations problem under harmonic pulsation of liquid pressure, i.e. harmonic vibrations of the upper channel wall. Using the perturbation method, we obtained the system of two integro-differential equations for studying the radial and flexural vibrations of the sandwich plate. Hydroelastic oscillations of the main mode were considered as a special case. The program for calculating the hydroelastic response of circular sandwich plate in various frequency ranges was developed. As an example, we made calculations of the circular sandwich plate amplitude-frequency response. The developed model can be applied in monitoring and decision-making systems for complex mechanical objects.