The interaction of instabilities in a hydroelastic system

The mutual effect of the bending of a thin elastic plate and the wave formation in the ideal incompressible liquids with dissimilar densities that are in contact over both of its surfaces is considered in the absence of surface tension. The plate is subjected to the action of a compressive force in its plane. The system is located in an acceleration field directed along the normal to the plane of the plate. A classification of the interactions of static Euler-Rayleigh instabilities and dynamic Lavrent'ev-Ishlinskii and Rayleigh-Taylor instabilities is given as well as the interaction of Koning-Taub and Richtmyer-Meshkov instabilities. Their special features are analysed.