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

Abstract

The article considers the problem of nonlinear oscillations of the motion of liquids completely filling an axisymmetric cylindrical vessel moving around a horizontal axis \(O{\kern 1pt} *{\kern 1pt} Y\). 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 finite rotational movements of the vessel is estimated and the case of 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 non-linear equations, found by the Bubnov-Galerkin method, was used in the article. As a result of the transformation, the amplitude-frequency characteristics and stability regions of a two-layer liquid are constructed under forced angular oscillations of a round cylindrical vessel.