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Free vibrations of a two-layer liquid in an elastic vessel

In the article we consider small motions of an ideal, non-compressible two-layer fluid with, divided by rigid permeable flat septum. Fluid fills the cylindrical tank with the sloping spherical bottom. The fluid motions we consider as potential. The velocity potential satisfies the Laplace equation. The resistance of the septum we assume linear with a constant coefficient of resistance. The effect of a permeable partition dividing the liquid column in the vessel is taken into account as a certain linearly viscous resistance with a reduced resistance coefficient specified as a parameter. The elasticity of the bottom of the vessel is taken into account by introducing the Airy function in the right-hand side of the differential equation corresponding to the movements of the elastic bottom.