Sloshing of Heterogeneous Liquid in Partially Filled Tanks: Example of a Vibration System without Compactness

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.