|
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 9, Pages 1710–1720
(Mi zvmmf118)
|
|
|
|
This article is cited in 4 scientific papers (total in 4 papers)
Effect of vertical vibrations on a two-layer system with a deformable interface
S. M. Zen'kovskaya, V. A. Novosyadlyĭ Southern Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090, Russia
Abstract:
The effect of single- and two-frequency vibrations on the behavior of a system consisting of two homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as a whole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order to analyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulation amplitudes is treated along with the case of high frequencies and small modulation amplitudes. In the former case, the parametric resonance domains are examined depending on the parameters of the system. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flattening the interface, and can suppress instability when the heavy fluid is over the light one.
Key words:
vibrations of a two-layer fluid, deformable interface, eigenvalue problem, Fourier analysis, continued fraction method.
Received: 03.08.2007 Revised: 11.11.2007
Citation:
S. M. Zen'kovskaya, V. A. Novosyadlyǐ, “Effect of vertical vibrations on a two-layer system with a deformable interface”, Zh. Vychisl. Mat. Mat. Fiz., 48:9 (2008), 1710–1720; Comput. Math. Math. Phys., 48:9 (2008), 1669–1679
Linking options:
https://www.mathnet.ru/eng/zvmmf118 https://www.mathnet.ru/eng/zvmmf/v48/i9/p1710
|
|