Response Regimes in Equivalent Mechanical Model of Strongly Nonlinear Liquid Sloshing

TL;DR

This paper develops an analytical model for liquid sloshing in tanks, capturing both linear and nonlinear regimes, including chaotic responses, validated through numerical simulations.

Contribution

It introduces an idealized vibro-impact system to model nonlinear sloshing, simplifying traditional high-power potential approaches for analytical exploration.

Findings

Steady-state and chaotic responses identified under external forcing.

Analytical predictions closely match numerical simulations.

Model effectively captures nonlinear and impact dynamics of liquid sloshing.

Abstract

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.