Free vibration of two identical circular plates coupled with bounded fluid

This paper examines the hydroelastic vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and the Rayleigh-Ritz method is suggested. In the theory, it is assumed that a rigid cylindrical container is filled with the ideal fluid and the two plates are clamped along the container edges. The proposed method is verified by finite element analysis using commercial software with excellent accuracy. Two transverse vibration modes, in-phase and out-of-phase, are observed alternately in the fluid-coupled system when the number of nodal circles increases for the fixed nodal diameter. It is found that the normalized natural frequency of the system monotonically increases with an increase in the number of nodal diameters and circles by virtue of a decrease in relative hydrodynamic mass.