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