Nonlinear Static and Dynamic Responses of a Floating Rod Pendulum

A novel nonlinear dynamics model is developed in this paper to describe the static and dynamic nonlinear behaviors of a rod pendulum partially immersed in still water. The pendulum is hinged above the water level (WL) and subject to nonlinear gravity, hydrostatic, and hydrodynamic loads, all of which are incorporated into the system dynamics. The nonlinear static behavior and stability of the pendulum have been characterized by analyzing the fixed points. It is found that Pitchfork bifurcation governs the relationship between the rod density (the control parameter) and the static equilibrium angle. The pendulum's nonlinear response to external harmonic torque is obtained using harmonic balance method (HBM). The influence of system parameters, including hinge height, rod diameter, and rod density, on the nonlinear frequency response is examined. Upon altering the system parameters, particularly the rod density, it is found that the system exhibits either a softening or a hardening effect.