Nonlinear static and dynamic behaviors of partially and fully submerged rod pendulums in quiescent water

This paper presents the development of a novel nonlinear dynamic model for partially and fully submerged rod pendulums. The pendulum undergoes oscillations in a quiescent water medium, wherein it experiences nonlinear hydrostatic and hydrodynamic forces that are integrated into the dynamics of the system. The analysis of the fixed points of the equation of motion is conducted to investigate the nonlinear static stability of the system and determine the static equilibrium angle. The static equilibrium characteristics exhibit a Pitchfork bifurcation, wherein the control parameter is the rod density ratio. The investigation also encompasses the examination of the impact of the depth and diameter ratios on the nonlinear static behavior. The investigation of the nonlinear frequency response to sinusoidal external torque applied to the hinge is subsequently carried out for the various potential equilibrium configurations. The investigation focuses on the influence of the system parameters, specifically the density, diameter, and depth ratios, across all configurations. The findings reveal that these parameters have varying effects.