Angular oscillations of solid bodies with a two-layer liquid near the main resonance

DOI: 10.34759/trd-2021-119-03

Аuthors

Win K. K.^*, Temnov A. N.^**

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: win.c.latt@gmail.com
**e-mail: antt45@mail.ru

Abstract

The development of rocket and space technology has led to the widespread use of cryogenic liquids, as a result of which it was proposed to create a certain stock of cryoproducts that are simultaneously in a two-phase or three-phase state, while forming layers of liquid, to increase their shelf life on board spacecraft or in tankers of future space refueling stations.

Nonlinear problems of the dynamics of a solid body having a cavity filled with several liquids are of considerable applied and theoretical interest. Many important problems of the dynamics of mechanical systems, including liquid masses with time-varying boundaries, lead to the need to solve the problem of the interaction of liquid with absolutely solid bodies. In particular, the linear equations of motion of a solid body with liquids will allow us to determine the change in the characteristics of the stability of motion due to the deformability of the free surface and the interface of the layered liquid.

The paper considers a problem in a nonlinear formulation about the vibrations of a solid body with an axisymmetric cavity around the horizontal axis OY and completely filled with two ideal and incompressible liquids. Nonlinear differential equations describing nonlinear oscillations of a solid body and the interface between two liquids in the vicinity of the main resonance of the vibrations of liquids are obtained. For a round cylindrical vessel, the hydrodynamic nonlinear problem is reduced to the sequential solution of linear boundary value problems. The obtained solutions of boundary value problems in the form of cylindrical functions were used to calculate linear and nonlinear hydrodynamic coefficients in the equations of oscillations of the mechanical system under consideration.

Keywords:

mechanical system, cylindrical cavity, hydrodynamic coefficients, basic resonance, perturbed surface, rotational motion

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