Interactions between the Euler, Helmholtz, and Rayleigh instabilities

The static bending of a thin plate that separates two liquids with different densities and velocities has been considered under the assumption that the liquids and the midsurface of the plate are incompressible. Wavelengths in this simple model are small compared to the sizes of the plate and liquid-filled spaces. Static interaction between the Euler, Helmholtz, and Rayleigh instabilities as a function of the compression force acting on the plate normally to the contact boundary has been studied. The ranges of the corresponding parameters have been found for the cases when the flatness of the plate and contact boundaries becomes stable and unstable.