Nonlinear vibrations of beams with Bouc–Wen hysteretic boundary conditions

In pressurized water reactors, the nuclear fuel rods are continuously subjected to turbulent fluid forces by the surrounding coolant. Flow-induced vibration of the fuel rod can lead to fretting wear between the rod and the spacer grid supports, with excessive wear resulting in a breach of the cladding and release of fission products to the reactor coolant system. Therefore, accurate modeling of the fuel rod dynamics is an important aspect of nuclear fuel assembly design. The spacer grids are constructed from thin, intersecting sheets of zirconium alloy welded into a square eggcrate-like pattern. Each cell of the spacer grid features stamped or inserted springs and stiff supports to restrain the fuel rod within the fuel assembly. The friction forces developed between the fuel rod and the compressed springs produce a nonlinear boundary condition which is responsible for the complex dynamic response of the fuel rod to external excitations. Nonlinear vibration experiments were performed on a single fuel rod supported at both ends by prototypic spacer grids to study the effect of the nonlinear boundary conditions on the rod response. The system was tested in quiescent water with a step-sine harmonic excitation. A model of the single fuel rod was developed to reproduce the measured nonlinear response. This made use of the Bouc–Wen hysteresis model to represent the nonlinear boundary condition imposed on the rod by the spacer grids. The rod is modeled as an Euler–Bernoulli beam taking into account fluid–structure interaction and structural damping. A good agreement between the model and the experimental results was obtained in the frequency and time domains for the applied forces considered.