Sloshing of Heterogeneous Liquid in Partially Filled Tanks: Example of a Vibration System without Compactness
Hilal Essaouini *
Departement of Physics, Abdelmalek Essaadi Universty, Faculty of Sciences, M2SM ER28/FS/05, 93000 Tetuan, Morocco.
Jalal Elbahaoui
Departement of Physics, Abdelmalek Essaadi Universty, Faculty of Sciences, M2SM ER28/FS/05, 93000 Tetuan, Morocco.
Larbi Elbakkali
Departement of Physics, Abdelmalek Essaadi Universty, Faculty of Sciences, M2SM ER28/FS/05, 93000 Tetuan, Morocco.
Pierre Capodanno
Franche-Comté University, 2B Rue des Jardins, 25000 Besançon, France.
*Author to whom correspondence should be addressed.
Abstract
The effect of the density of the liquid on the sloshing in partially filled tanks is studied. The liquid is assumed to be almost-homogeneous (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant). In this case the linearized Euler’s equation of the liquid is presented and analyzed, the relevant operators are studied. The Weyl’s criterion is used for computing the spectrum of the fundamental operator . We obtain nonclassically spectrum with continuous part filling an interval.
Keywords: Heterogeneous liquid, sloshing, Weyl’s criterion, essential spectrum.