Linear Mechatronic Modeling of Rectangular Tank Sloshing Dynamics

ABSTRACT

Sloshing dynamics in partially filled tanks can strongly influence system‐level behavior when fluid motion couples with rigid‐body dynamics. This paper presents a linear and acausal two‐dimensional sloshing model for rectangular tanks, based on the reformulation of established sloshing theory within a modular, multi‐domain modeling framework, applicable to mechatronic systems. The model resolves sway‐ and roll‐induced sloshing and incorporates heave motion which, unlike traditional linear equivalent mechanical systems, account for pressure loading under multi‐axis excitation. All coefficients are derived directly from tank geometry and fluid properties, requiring no model identification. Mixed causality, here referring to any combination of force and velocity inputs to the model, are supported without introducing dependent states. The model is based on a modal decomposition of free‐surface standing waves under the assumptions of linear potential flow theory. Bond graph and state‐space representations are presented. Applications include tuned liquid dampers, low‐amplitude ship motion, and tanks mounted on motion‐controlled platforms. A steepness‐based criterion is used as a real‐time indication of model validity. Established sloshing theory is utilized to evaluate model range of validity and damping. Experimental steady‐state validation is conducted using a suspended water pendulum configuration, with predicted oscillation periods closely matching measured values under moderate initial displacements. The proposed formulation provides a computationally efficient, system‐level representation of sloshing dynamics for multi‐axis applications within the linear regime.