Geodesic
Effect of vertical vibrations on a two-layer system with a deformable interface
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1710-1720

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZVMMF_2008_48_9_a14,
     author = {S. M. Zen'kovskaya and V. A. Novosyadlyǐ},
     title = {Effect of vertical vibrations on a~two-layer system with a~deformable interface},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1710--1720},
     publisher = {mathdoc},
     volume = {48},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a14/}
}
TY  - JOUR
AU  - S. M. Zen'kovskaya
AU  - V. A. Novosyadlyǐ
TI  - Effect of vertical vibrations on a two-layer system with a deformable interface
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1710
EP  - 1720
VL  - 48
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a14/
LA  - ru
ID  - ZVMMF_2008_48_9_a14
ER  - 
%0 Journal Article
%A S. M. Zen'kovskaya
%A V. A. Novosyadlyǐ
%T Effect of vertical vibrations on a two-layer system with a deformable interface
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1710-1720
%V 48
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a14/
%G ru
%F ZVMMF_2008_48_9_a14
S. M. Zen'kovskaya; V. A. Novosyadlyǐ. Effect of vertical vibrations on a two-layer system with a deformable interface. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1710-1720. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a14/