Nonlinear Vibrations of Model PWR Fuel Assemblies: Part 2 — Interpretation of Results Using Bilinear Stiffness Model

Abstract The experimental response of fuel rods with spacer grids was interpreted using a bilinear hysteresis model. Nonlinear experimental responses of two configurations of rods made out of Zirconium alloy tubes were considered in this paper: one configuration with a single beam and the second configuration with a cluster of beams (stacked in a 3 × 3 matrix formulation). These two configurations were designed to emulate part of the nuclear fuel assembly in Pressurized Water Reactors (PWR). Both configurations were supported by spacer girds at their extremities and were immersed in still water. Spacer grids are grid-like structures made out of thin Zirconium alloy sheets with 17 × 17 cells arranged in a square pattern. Spacer grids provide mechanical support and reduce flow-induced vibration of nuclear fuel rods. They also improve the heat transfer between nuclear fuel rods and the surrounding coolant. The spacer grids impose nonlinear boundary conditions to the beams at the contact points/surface. Specifically, spacer grids present bilinear hysteresis due to their inherent complexity. The bilinear hysteresis shown by spacer grids was measured in terms of force-displacement loops by testing rigid rod inserted in one of its cells. The rigid rod was then excited by external harmonic excitation with excitation frequencies ranging from 5 Hz to 50 Hz in steps of 5 Hz. The bilinear hysteresis model, first studied by Caughey, was modified to include viscous damping and was used to interpret the experimental results. The method of slowly varying parameters was used to solve the equation of motion. First, the measured force-displacement loops of spacer grids were fitted with the numerical model described in the current analysis. Good agreement between the model response and measured loops was found, and the identified parameters allowed the characterization of the nonlinear boundary conditions imposed by spacer grids. Finally, the nonlinear responses of the two configurations under study were interpreted using the bilinear hysteresis model. Excellent agreement between numerical and experimental results was obtained for both configurations.