An analytical method for free vibrations of the fuel rod with non-uniform mass of small modular reactor

Abstract

The intricate internal structure of fuel rods results in a non-uniform mass distribution, making it imperative to employ analytical methods for accurate assessment. The study utilizes Euler beam theory to derive the transverse vibration equation for beams with varying mass distribution. The approach involves transforming the non-uniform mass beam into a multi-segment beam with concentrated mass points. Modal function relationships between adjacent uniform segments are established based on continuous conditions at connection points. This transformation leads to the conversion of the variable coefficient differential equation into a nonlinear matrix equation. The Newton-Raphson method is then applied to calculate the characteristic equation and mode shapes, essential for determining natural frequencies. To validate precision, the results obtained are compared with those derived from the finite element method. Furthermore, the developed method is employed to assess the impact of gas plenum location and length on the natural frequency of fuel rods. The proposed methodology serves as a rapid design tool, particularly beneficial during the design phase of fuel rods with non-uniform mass distribution, aiding in configuring structural aspects effectively.