Free vibration of multiple rectangular plates coupled with a liquid

Fuel assemblies of a research reactor consist of a number of rectangular fuel plates with an equal gap and the coolant flows between the fuel plates for heat exchange. The paper deals with a theoretical dynamic model of the fuel assembly submerged in the coolant, and presents a free vibration analysis of a bundle of identical rectangular plates fully in contact with an ideal liquid. The orthogonal polynomial functions, as admissible functions, were generated using the Gram–Schmidt process to approximate the wet dynamic displacements of the plates with a clamped-clamped-free-free boundary condition. The liquid displacement potential satisfying the boundary conditions was derived, and the wet dynamic modal functions of the plates were expanded by the finite Fourier transform for a compatibility requirement along the contacting surface between the plates and the liquid. The natural frequencies under the wet condition were calculated using the Rayleigh–Ritz method based on minimizing the Rayleigh quotient of the ratio between the maximum potential energy and total kinetic energy. The comparison showed excellent agreement between the results from the proposed theoretical method with the finite element analysis results. The effect of the liquid gap between the plates on the normalized natural frequencies was discussed.