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A dynamical system involving a driven pendulum filled with liquid, isanalyzed in the present paper series. The study of such a system is conductedin order to understand energy dissipation resulting from the shallow watersloshing and induced wave breaking. This analysis is relevant for the design ofTuned Liquid Damper devices. The complexity and violence of the flow generatedby the roll motion results in the impossibility of using an analyticalapproach, requiring in turn the use of a suitable numerical solver. In Part I,the coupled dynamical system is thoroughly described, revealing its nonlinearfeatures associated with the large amplitude of the forcing, both in terms ofmechanical and fluid dynamical aspects. A smoothed particle hydrodynamics (SPH)model, largely validated in literature, is used to calculate the frequencybehavior of the whole system. For small rotation angles, a semi-analyticalmodel of the energy dissipated by the fluid, based on a hydraulic jumpsolution, is developed; the energy transfer is numerically calculated in orderto extend the analysis to large oscillation angles. The experimental part ofthe investigation is carried out in Part II of this work.

physics of fluids

Mechanical energy dissipation induced by sloshing and wave breaking in a  fully coupled angular motion system. Part I: Theoretical formulation and  Numerical Investigation