Lymar O. Oscillations of a rectangular plate separating liquids of different density in a rectangular channel with elastic bases

The thesis is devoted to the study of natural oscillations and stability of a rectangular plate, horizontally separating ideal incompressible fluids of different densities in a rigid rectangular channel with two rigid bases, with one rigid and the other elastic and with two elastic bases in the form of rectangular plates. These studies are based on the construction of an analytical solution for joint oscillations of plates and liquids. Combined vibrations of elastic plates and fluids are reduced to a system of integro-differential equations, and the plate deflection forms are provided as a sum of the fundamental solutions of a homogeneous equation for a plate and a particular solution of a non-homogeneous one in the form of an eigenfluid fluid expansion in a rectangular channel An analytical solution of the natural oscillation problems of a rectangular plate obtained in a linear formulation horizontally separates ideal incompressible liquids of different densities in a rigid rectangular channel with two rigid bases, one elastic, and the second rigid and two elastic bases. All plates can have arbitrary fixing contours. For two clamped, supported and free contours of the plates, the simplification of the frequency equations carried out. The greatest simplification was made only for the clamped plates. From the dynamic and static approaches, approximate and exact conditions for the stability of oscillations for a clamped plate in a channel with two rigid bases are obtained. Approximate and exact conditions for the stability of oscillations for clamped plates in a channel with one elastic and the second rigid bases are derived. It is shown that in the case of two elastic bases, the frequency spectrum of asymmetrical oscillations will consist of three sets of frequencies corresponding to the vibrations of the three plates, and the frequency spectrum of the symmetric oscillations will consist of four sets of frequencies corresponding to the vibrations of the three plates and the oscillation of the liquid column as a whole. Numerical studies of the static problem are carried out and limitations are found on the dimensionless mechanical parameters under which the deflections of the plates remain in the framework of the linear theory, which is a necessary condition for the dynamic problem. Analytical and numerical studies conducted in this work showed a fairly high efficiency of the simplified frequency equations and stability conditions obtained. The reliability of a part of the obtained results is confirmed by comparison with results known in the literature.