Linearised metamodel for two-dimensional sloshing effects in partially-filled rectangular tanks under horizontal excitation

Sloshing dynamics in partially-filled rectangular tanks remains a computationally demanding phenomenon in applications such as tuned liquid dampers, largely due to high computational costs of using high-fidelity sloshing models. Additionally, the effective damping of coupled dynamic systems is challenging to describe with existent equivalent or reduced-order sloshing models. This article introduces a linearised force-based modelling strategy by using time-domain approach, that constructs equivalent mass and damping derivatives for the sloshing effect under horizontal excitation. The proposed formulation derives closed-form linearised force expressions calibrated on high-fidelity sloshing analysis and incorporates them into a reduced-order dynamic system. In this way, the method preserves key hydrodynamic behaviour while significantly decreases the numerical cost. The sloshing derivatives are estimated based on the tank geometry, excitation, amplitude, and frequency characteristics, with model assumptions focused on stationary oscillatory conditions. Benchmark comparisons against conventional numerical sloshing simulations demonstrate a substantial reduction in computational time and a close agreement in the overall dynamic response. Owing to its efficiency and robustness, the proposed model provides a pathway for accelerating surrogate-based analyses in coupled applications for structure dynamics--TLD interactions and pre-design workflows for practical purposes.