Internal Resonances and Dynamic Responses in Equivalent Mechanical Model of Partially Liquid-Filled Vessel

Abstract

This study treats oscillations of a liquid in partially filled vessel under horizontal harmonic ground excitation. When exposed to external disturbances, the liquid is divided into two portions: oscillating sloshing portion, and a-’static’ non-sloshing portion, located at the bottom of the tank. Such excitation may lead to hydraulic impacts applied by the sloshing mass on the tank walls.Different equivalent mechanical models are suggested to mimic the liquid sloshing mass motion and essential dynamical regimes of the overall tank-liquid system, such as a series of pendula or mass-spring-dashpot systems which can impact the vessel walls. We use parameters of the equivalent mass-spring system for the well-explored case of cylindrical vessels. The hydraulic impacts are modeled by high-power potential function. Finite-Element (FE) method is used to determine and verify the model parameters and to identify dominant dynamical regimes, natural modes and frequencies. The tank failure modes and critical locations are identified. Mathematical relation is found between degrees-of-freedom (DOFs) motion and the mechanical stress applied in the tank critical section. This is the prior attempt to take under consideration large-amplitude nonlinear sloshing and tank structure elasticity effects for design, regulation definition and resistance analysis purposes. Both linear (tuned mass damper, TMD) and nonlinear (nonlinear energy sink, NES) passive energy absorbers contribution to the overall system mitigation is firstly examined.