Description of interaction problem between sloshing and structure by using constraints

Abstract

This study addresses the coupled behavior between sloshing in a tank and a structure. It is motivated by design of liquid storage tanks, liquid cargo transportations, tuned liquid dampers, and so on. In particular, this paper focuses on development of coupling strategy based on the Hamiltonian mechanics for the constraint system with the Lagrange's method of undetermined multipliers. As a result of this formulation, it can be found that equations of motion of this system is given by the differential algebraic equations (DAEs) consisting of differential equations for the sloshing and the structure and an algebraic equation (constraint) for the momentum of structure motion and the liquid surface displacement. In order to calculate the DAEs formulated by the present method, this study employed a numerical integration technique based on the energy–momentum method. The proposed approach is validated by comparisons with an existing model and an experiment in the time domain analysis.