Research of Amplitude-Frequency Characteristics of Nonlinear Oscillations of the Interface of Two-Layered Liquid
The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3669196Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 113
 Hutton R. E. “An investigation of non-linear, nonplanar oscillations of fluid in cylindrical container” Techn. Note. – Washington. (NASA; D-1870). – 1963- P. 191-194.
 Chu W.H., Kana D.D. “A theory for nonlinear transverse vibrations of a partially filled ellastic tank” J. Appl. Mech., -1967. – 5, N 10. – P. 1828-1835.
 Thorpe S.A. “On standing internal gravity waves of finite amplitude”-J. Fluid Mech. 1968. v. 32, № 3, p. 489-528. (DOI: https://doi.org/10.1017/S002211206800087X)
 Sekerzh-Zen’kovich S. Y. “The free oscillations of a viscous two-layer fluid in a closed vessel” Journal of Applied Mathematics and Mechanics. -1990. — Vol. 54, no. 1. — P. 39–45.
 Win Ko Ko, Temnov A. N. “Experimental and theoretical studies of oscillations of stratified fluid” IOP Conference Series: Materials Science and Engineering 468 (2018) 012031.
 Porubov A. V. “Localization of two-dimensional nonlinear internal waves in two-layer fluid” Doklady physics. 2005, Volume 75, vol. 7.
 Kalinichenko. V. A., Sekerzh-Zenkovich S. Ya., Timofeev A. S. “Experimental investigation of the velocity field of parametrically excited waves in a two-layer liquid” Izv. USSR Academy of Sciences. MIG. 1991. No. 5. p. 161-166.
 Sretenskiy L.N. Teoriya volnovykh dvizheniy zhidkosti (Wave flow theory of the liquid). Moscow, Nauka Publ., 1977. 815 p.
 Landau L.D., Lifshits E.M. Teoreticheskaya fizika. Tom VI. Gidrodinamika (Theoretical physics. Vol. VI. Hydrodynamics). Moscow, Nauka Publ., 1986, 735 p.
 WIN Ko Ko, Temnov A. N. “Oscillations of discrete stratified liquids in a cylindrical vessel and their mechanical analogues” Vestnik MGTU im. Bauman's. Ser. “Natural science.” No. 3. p. 57-69.
 WIN Ko Ko, Temnov A. N. “Experimental and theoretical study of oscillations of a solid body with a layered liquid” Engineering journal: science and innovation, Moscow state technical University. N. E. Bauman. Electron. journal., No. 04, 2018. p. 1-13.
 WIN Ko Ko, Temnov A. N. “Theoretical and experimental studies of vibrations of the solid half-cylinder having a cavity filled with a layered fluid” Inzhenernyy zhurnal: nauka i innovatsiya—Engineering Journal: Science and Innovation, Moscow state technical University. N. E. Bauman. Electron. Journal, 2019, iss. 05(89). p. 1-16. (DOI: 10.18698/2308-6033-2019-5-1883)
 WIN Ko Ko, Temnov A. N. “Oscillations of a three-layer viscous liquid in a stationary tank” Inzhenernyy zhurnal: nauka i innovatsiya —Engineering Journal: Science and Innovation, Moscow state technical University. N. E. Bauman. Electron. journal, 2019, iss. 07(91). p. 1-17. (DOI: 10.18698/2308-6033-2019-7-1895)
 Lukovsky I.A. Introduction to nonlinear dynamics of a solid with cavities containing a liquid; Rev. Ed. V. A. Trotsenko; Ukrainian Academy of Sciences. In-t of mathematics. - Kyiv: Nauk. Dumka, 1990.-296 p. - ISBN 5-12-001308-2.
 Narimanov G. S., Dokuchaev L. V., Lukovsky I. A. Nonlinear dynamics of an aircraft with a liquid. M., "Mechanical engineering", 1977, 208 p.
 Mikishev. G. N. Experimental methods in spacecraft dynamics. - M.: Mechanical engineering, 1987. 248 p.
 Mikishev. G. N., Rabinovich B. И. Dynamics of a solid body with cavities filled with fluid. - M.: Mechanical engineering, 1968. - 532 P.