Internal resonances and dynamic responses in equivalent mechanical model of partially liquid-filled vessel

TL;DR

This study models the oscillations of liquid in a partially filled vessel under horizontal excitation, analyzing internal resonances, impacts, and multiple steady states using an equivalent pendulum approach.

Contribution

It introduces a novel equivalent pendulum model for liquid sloshing in cylindrical vessels and explores internal resonance conditions and dynamic responses.

Findings

Identification of conditions for internal resonances.

Existence of multiple steady states beyond critical excitation.

Presence of quasi-periodic solutions in narrow parameter ranges.

Abstract

The paper treats oscillations of a liquid in partially filled vessel under horizontal harmonic ground excitation. Such excitation may lead to hydraulic impacts. The liquid sloshing mass is modeled by equivalent pendulum, which can impact the vessel walls. We use parameters of the equivalent pendulum for well-explored case of cylindrical vessels. The hydraulic impacts are modeled by high-power potential function. Conditions for internal resonances are presented. A non-resonant behavior and dynamic response related to 3:1 internal resonance are explored. When the excitation amplitude exceeds a critical value, the system exhibits multiple steady state solutions. Quasi-periodic solutions appear in relatively narrow range of parameters. Numerical continuation links between resonant regimes found asymptotically for small excitation amplitude, and high-amplitude responses with intensive impacts.