Character of force interaction of an ideal liquid with a free surface in the ellipsoidal reservoir of revolution

Abstract

Theproblemofforcednonlinearcombinedmotionofthereservoirofellipsoidalrevolutionandavolumeofidealliqui
dwithafreesurfaceisunderconsideration. Mathematical model of the problem is constructed based on the
Hamilton–Ostrogradsky variational principle with using approaches of nonlinear mechanics and the
Kantorovich method. Finally, this enables the construction of nonlinear dynamic model of the system in the
form of a system of ordinary differential equations relative to amplitudes of excitations of normal modes of
oscillation of a liquid and parameters of translational motion of the reservoir. For different disturbance
frequencies of the system motion in a vicinity of the first resonance we determined characteristics of the
force interaction of a liquid with the reservoir depending on inclination of reservoir walls and degrees of
filling the reservoir by a liquid. It was ascertained that to certain extent dependencies of variation of force
characteristics coincide with variations of elevations of a liquid free surface