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In Pressurized Water Reactors (PWR), fuel assemblies are made up 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 nonlinear response of the structure, and, particularly, its dissipation, is of paramount importance for the choice of safety margins, in the design of fuel assemblies, to ensure their functionality and safety in the worst external condition scenarios. To model the nonlinear dynamic response of fuel rods, the identification of the nonlinear stiffness and damping parameters is required. A tool based on harmonic balance method was developed to identify these parameters from the experimentally obtained force-response curves, considering one-to-one internal resonance phenomenon present in axisymmetric structures such as cylindrical tubes and shells. To validate the tool, it was applied to the reference case of circular cylindrical shell filled with water, which revealed an increase of damping with the excitation amplitude. In the following paper, the more realistic case of a single fuel rod with clamped-clamped boundary condition was investigated by applying harmonic excitation at various force levels. The nonlinear parameters including damping were extracted from experimental results by means of the adapted tool. An increase in damping with excitation amplitude has been shown according to earlier studies.