In pressurized water reactors (PWR), grid to rod fretting (GTRF) is a primary cause of fuel failure due to fuel rod vibrations. Understanding and characterizing the dynamics of fuel rods is essential for analyzing GTRF and ensuring reactor safety.

This study aims to develop a vibration analysis method that can reasonably represent the dynamics of fuel rods within a reactor, focusing on the vibration characteristics of fuel rods supported by multiple positioning grids.

Firstly, a mechanical model was established for a multi-span elastically supported fuel rod restrained by multiple sets of positioning grids. The restraint effect of the grids was simplified into tension and compression springs and torsion springs within the elastic range. Then, a displacement function based on an improved Fourier series was constructed for the whole beam section, and the modal state was solved using the energy principal method. Subsequently, the Improved Fourier Series Method (IFSM) was used to address boundary discontinuity issues, eliminating the need to reconstruct the model for structural and boundary changes. Finally, the accuracy of this method was verified by comparing with the finite element calculation results, and the vibration characteristics of fuel rods were analyzed.

The results show that the tension spring stiffness is the dominant factor influencing the overall variation pattern of the intrinsic vibration frequency of the fuel rod. The influence of the torsion spring on the vibration characteristics is dependent on the tension spring stiffness, with minimal impact when the tension spring stiffness is small. Changes in boundary conditions affect the system's stiffness, which in turn influences modal frequency. Increased overall stiffness leads to increased deformation resistance and higher modal frequency.

The study concludes that the strength of the restraint effect of the spacer grid on the fuel rod significantly influences the vibration characteristics of the fuel rod under multi-span elastic support. The developed method provides a reliable tool for analyzing the vibration characteristics of fuel rods with multiple grid constraints, which can be used as a reference in practical engineering applications.