An analytical method for free vibrations of the fuel rod with non-uniform mass of small modular reactor - Yang, Guowei; Zhang, Yong; Fan, Tiandi; Song, Yong; Bai, Yunqing (Frontiers in Energy Research, 2024)
Structural stability analysis is an essential part of the fuel rod design. Due to the intricate internal structure, the fuel rod exhibits non-uniform mass distribution. Using Euler beam theory, the transverse vibration equation was derived for beams with varying mass distribution. By equivalently transforming the non-uniform mass beam into a multi-segment beam with concentrated mass points, modal function relationships between adjacent uniform segments were established based on continuous conditions at connection points. The variable coefficient differential equation was transformed into a nonlinear matrix equation. The Newton-Raphson method was employed to calculate the characteristic equation and mode shapes for determining natural frequencies.Precision was ensured through comparison with finite element method results.Subsequently, this method is employed to evaluate the impact of gas plenum location and length on fuel rod natural frequency. It serves as a rapid design tool for configuring structural aspects during the design phase, particularly for fuel rods with non-uniform mass distribution.