Eigen oscillations of the elastic bottom of a cylindrical vessel and liquid with a free surface
The object of research is the cylindrical vessel of arbitrary cross section with a rigid lateral surface and a flat elastic bottom. The vessel is filled by an ideal incompressible liquid. The problem of the joint fluctuations of the flat bottom and the fluid is solved in a linear formulation. Bottom of the vessel and the liquid is considered to be of attached, and motion of a liquid is invortial. The condition of solvability of the system is satisfied. General solution is obtained, the frequency equations and their own forms of joint oscillations were found. This allows us to consider a more important problem of forced vibrations of mechanical systems.
scientific article; zbMATH DE number 6062269