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

The experimental response of beams with nonlinear boundary conditions was interpreted using a bilinear hysteresis model.  Nonlinear experimental responses of two configurations of beams 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 3x3 matrix formulation). These two configurations were designed to emulate part of the nuclear fuel assembly in Pressurized Water Reactors (PWR). Both the configurations were supported by spacer girds at both ends and immersed in still water. Spacer grids are grid-like structures made out of thin Zirconium alloy sheets with 17x17 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 under study here. Specifically, spacer grids present bilinear hysteresis due to its inherent complexity. The bilinear hysteresis shown by spacer grids were measured in terms of force-displacement loops by inserting a rigid rod in one of its cells. The rigid rod was then excited with harmonic excitation 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 model developed here and found very good agreement. The identified parameters allowed us to characterize the nonlinear boundary conditions imposed by spacer grids. The bilinear parameter increases with vibration amplitude.  Finally, the nonlinear responses of two configurations under study were interpreted using the bilinear hysteresis model. Excellent agreement between numerical and experimental results was obtained for both the configurations. The model captures the unsymmetrical frequency response curves and softening behavior of simplified nuclear fuel assembly models. Hence, the model can be said to be well suited for studying nonlinear vibrations of the nuclear fuel assembly. The boundary conditions change from being linear at low vibration amplitudes to being bilinear with hysteresis at higher vibration amplitudes. The overall stiffness of the boundary condition decreases with increasing vibration amplitude. In addition, the equivalent damping of the system increases with vibration amplitude. The development of reduced-order models of beams with bilinear hysteresis at the boundary is left for a future study.