  We consider equivalent mechanical model of liquid sloshing in
partially-filled cylindrical vessel; the model treats both the regime of linear
sloshing, and strongly nonlinear sloshing regime. The latter is related to
hydraulic impacts applied to the vessel walls. These hydraulic impacts are
commonly simulated with the help of high-power potential and dissipation
functions. For the sake of analytic exploration, we substitute this traditional
approach by treatment of an idealized vibro-impact system with
velocity-dependent restitution coefficient. The obtained reduced model is
similar to recently explored system of linear primary oscillator with attached
vibro-impact energy sink. The ratio of modal mass of the first sloshing mode to
the total mass of the liquid and the tank serves as a natural small parameter
for multiple-scale analysis. In the case of external ground forcing,
steady-state responses and chaotic strongly modulated responses are revealed.
All analytical predictions of the reduced vibro-impact model are validated
against direct numerical simulations of initial equivalent model with
high-power smooth potential and dissipation functions, and good agreement is
observed.
