In Pressurized Water Reactors (PWR), fuel assemblies are composed of fuel rods, long slender tubes filled with uranium pellets, bundled together using spacer grids. These structures are subjected to fluid-structure interactions, due to the flowing coolant surrounding the fuel assemblies inside the core, coupled with large-amplitude vibrations in case of external seismic excitation. Therefore, understanding the non-linear response of the structure and, particularly, its dissipation, is of paramount importance for the choice of safety margins. To model the nonlinear dynamic response of fuel rods, the identification of nonlinear stiffness and damping parameters is required. The case of a single fuel rod with clamped-clamped boundary conditions was investigated by applying harmonic excitation at various force levels. Different configurations were implemented testing the fuel rod in air and in still water; the effect of metal pellets simulating nuclear fuel pellets inside the rods was also recorded. Non-linear parameters were extracted from some of the experimental response curves by means of a numerical tool based on the harmonic balance method. The axisymmetric geometry of fuel rods resulted in the presence of a one-to-one internal resonance phenomenon, which has to be taken into account modifying accordingly the numerical identification tool. The internal motion of fuel pellets is a cause of friction and impacts, complicating further the linear and non-linear dynamic behavior of the system. An increase of the equivalent viscous-based modal damping with excitation amplitude is often shown during geometrically non-linear vibrations, thus confirming previous experimental findings in the literature.