Amplitude–Frequency Characteristics and Stability Regions of a Two-Layer Liquid under the Angular Vibrations of a Solid Body

This article considers the problem of nonlinear oscillations of the motion of liquids completely filling an axisymmetric cylindrical vessel moving around the horizontal \(O{\kern 1pt} \text{*}{\kern 1pt} Y\) axis. The motion of each fluid is assumed to be potential and formulated in a cylindrical coordinate system. The influence of nonlinear coefficients on the characteristics of dynamic processes during the finite rotational motions of the vessel is estimated and the case of the forced angular oscillations of a vessel with liquids relative to a fixed axis is considered. The main nonlinear effects associated with the rotation of the diameter of the interface of liquids are also revealed. An approximate solution of the obtained nonlinear equations, found by the Bubnov–Galerkin method, is used in the article. As a result of the transformation, the amplitude-frequency characteristics (AFC) and stability regions of a two-layer liquid are constructed under the forced angular oscillations of a round cylindrical vessel.